diff --git a/candle-core/src/backprop.rs b/candle-core/src/backprop.rs
index a44f732f..46a2c8de 100644
--- a/candle-core/src/backprop.rs
+++ b/candle-core/src/backprop.rs
@@ -76,6 +76,7 @@ impl Tensor {
                     | Op::Sqrt(node)
                     | Op::Gelu(node)
                     | Op::Relu(node)
+                    | Op::Elu(node, _)
                     | Op::Exp(node)
                     | Op::Log(node)
                     | Op::Sin(node)
@@ -250,6 +251,7 @@ impl Tensor {
                     }
                     Op::Gelu(_) => return Err(Error::BackwardNotSupported { op: "gelu" }),
                     Op::Relu(_) => return Err(Error::BackwardNotSupported { op: "relu" }),
+                    Op::Elu(..) => return Err(Error::BackwardNotSupported { op: "elu" }),
                     Op::Sqr(arg) => {
                         let arg_grad = arg.mul(&grad)?.affine(2., 0.)?;
                         let sum_grad = grads.or_insert(arg)?;
diff --git a/candle-core/src/cpu_backend.rs b/candle-core/src/cpu_backend.rs
index 6d1cea3b..15982040 100644
--- a/candle-core/src/cpu_backend.rs
+++ b/candle-core/src/cpu_backend.rs
@@ -463,6 +463,14 @@ fn divide_by_sum_over_dim<T: WithDType>(s: &mut [T], shape: &Shape, dim: usize)
     Ok(())
 }
 
+fn elu<T: num_traits::Float>(v: T, alpha: T) -> T {
+    if v.is_sign_positive() {
+        v
+    } else {
+        (v.exp() - T::one()) * alpha
+    }
+}
+
 impl CpuStorage {
     pub fn dtype(&self) -> DType {
         match self {
@@ -666,6 +674,30 @@ impl CpuStorage {
         Affine(mul, add).map(self, layout)
     }
 
+    pub(crate) fn elu(&self, layout: &Layout, alpha: f64) -> Result<Self> {
+        // TODO: Have some generic map for functions that apply on num_traits::Float elements.
+        match self {
+            Self::BF16(storage) => {
+                let data = unary_map(storage, layout, |v| elu(v, bf16::from_f64(alpha)));
+                Ok(Self::BF16(data))
+            }
+            Self::F16(storage) => {
+                let data = unary_map(storage, layout, |v| elu(v, f16::from_f64(alpha)));
+                Ok(Self::F16(data))
+            }
+            Self::F32(storage) => {
+                let data = unary_map(storage, layout, |v| elu(v, f32::from_f64(alpha)));
+                Ok(Self::F32(data))
+            }
+            Self::F64(storage) => {
+                let data = unary_map(storage, layout, |v| elu(v, alpha));
+                Ok(Self::F64(data))
+            }
+            Self::U8(_) => Err(Error::UnsupportedDTypeForOp(DType::U8, "elu")),
+            Self::U32(_) => Err(Error::UnsupportedDTypeForOp(DType::U32, "elu")),
+        }
+    }
+
     pub(crate) fn unary_impl<B: UnaryOp>(&self, layout: &Layout) -> Result<Self> {
         match self {
             Self::BF16(storage) => {
diff --git a/candle-core/src/cuda_backend.rs b/candle-core/src/cuda_backend.rs
index 3df34cee..3df1b33c 100644
--- a/candle-core/src/cuda_backend.rs
+++ b/candle-core/src/cuda_backend.rs
@@ -357,6 +357,30 @@ impl Map1 for Affine {
     }
 }
 
+struct Elu(f64);
+impl Map1 for Elu {
+    fn f<T: DeviceRepr + WithDType>(
+        &self,
+        src: &CudaSlice<T>,
+        dev: &CudaDevice,
+        layout: &Layout,
+    ) -> Result<CudaSlice<T>> {
+        let shape = layout.shape();
+        let dims = shape.dims();
+        let el = shape.elem_count();
+        let cfg = LaunchConfig::for_num_elems(el as u32);
+        let ds = dev.htod_copy([dims, layout.stride()].concat())?;
+        let src = &src.slice(layout.start_offset()..);
+        let func = dev.get_or_load_func(&kernel_name::<T>("uelu"), kernels::UNARY)?;
+        // SAFETY: Set later by running the kernel.
+        let out = unsafe { dev.alloc::<T>(el) }?;
+        let params = (el, dims.len(), &ds, T::from_f64(self.0), src, &out);
+        // SAFETY: ffi.
+        unsafe { func.launch(cfg, params) }?;
+        Ok(out)
+    }
+}
+
 #[allow(dead_code)]
 struct Sum<'a>(&'a [usize]);
 impl<'a> Map1 for Sum<'a> {
@@ -815,6 +839,12 @@ impl CudaStorage {
         Ok(Self { slice, device })
     }
 
+    pub(crate) fn elu(&self, layout: &Layout, alpha: f64) -> Result<Self> {
+        let device = self.device().clone();
+        let slice = Elu(alpha).map(&self.slice, &device, layout)?;
+        Ok(Self { slice, device })
+    }
+
     pub(crate) fn sum(&self, layout: &Layout, sum_dims: &[usize]) -> Result<Self> {
         let device = self.device().clone();
         let slice = FastSum(sum_dims).map(&self.slice, &device, layout)?;
diff --git a/candle-core/src/dummy_cuda_backend.rs b/candle-core/src/dummy_cuda_backend.rs
index 0dbd8d54..9263adee 100644
--- a/candle-core/src/dummy_cuda_backend.rs
+++ b/candle-core/src/dummy_cuda_backend.rs
@@ -64,6 +64,10 @@ impl CudaStorage {
         Err(Error::NotCompiledWithCudaSupport)
     }
 
+    pub(crate) fn elu(&self, _: &Layout, _: f64) -> Result<Self> {
+        Err(Error::NotCompiledWithCudaSupport)
+    }
+
     pub(crate) fn sum(&self, _: &Layout, _: &[usize]) -> Result<Self> {
         Err(Error::NotCompiledWithCudaSupport)
     }
diff --git a/candle-core/src/error.rs b/candle-core/src/error.rs
index 9f12b9a2..d8f3b4b4 100644
--- a/candle-core/src/error.rs
+++ b/candle-core/src/error.rs
@@ -127,6 +127,9 @@ pub enum Error {
     #[error("unsupported safetensor dtype {0:?}")]
     UnsupportedSafeTensorDtype(safetensors::Dtype),
 
+    #[error("unsupported dtype {0:?} for op {1}")]
+    UnsupportedDTypeForOp(DType, &'static str),
+
     #[error("cannot broadcast {src_shape:?} to {dst_shape:?}")]
     BroadcastIncompatibleShapes { src_shape: Shape, dst_shape: Shape },
 
diff --git a/candle-core/src/op.rs b/candle-core/src/op.rs
index ee57b325..1b2d800d 100644
--- a/candle-core/src/op.rs
+++ b/candle-core/src/op.rs
@@ -46,6 +46,7 @@ pub(crate) enum Op {
     Transpose(Tensor, usize, usize),
     Gelu(Tensor),
     Relu(Tensor),
+    Elu(Tensor, f64),
     // TODO: Support for custom ops.
 }
 
diff --git a/candle-core/src/storage.rs b/candle-core/src/storage.rs
index 53ea1544..ee12eeb8 100644
--- a/candle-core/src/storage.rs
+++ b/candle-core/src/storage.rs
@@ -66,6 +66,19 @@ impl Storage {
         }
     }
 
+    pub(crate) fn elu(&self, layout: &Layout, alpha: f64) -> Result<Self> {
+        match self {
+            Storage::Cpu(storage) => {
+                let storage = storage.elu(layout, alpha)?;
+                Ok(Self::Cpu(storage))
+            }
+            Self::Cuda(storage) => {
+                let storage = storage.elu(layout, alpha)?;
+                Ok(Self::Cuda(storage))
+            }
+        }
+    }
+
     pub(crate) fn sum(&self, layout: &Layout, s: &[usize]) -> Result<Self> {
         match self {
             Storage::Cpu(storage) => {
diff --git a/candle-core/src/tensor.rs b/candle-core/src/tensor.rs
index 6f8dc378..f0ce18f9 100644
--- a/candle-core/src/tensor.rs
+++ b/candle-core/src/tensor.rs
@@ -349,6 +349,16 @@ impl Tensor {
         Ok(from_storage(storage, self.shape(), op, false))
     }
 
+    pub fn elu(&self, alpha: f64) -> Result<Self> {
+        let storage = self.storage.elu(self.layout(), alpha)?;
+        let op = if self.track_op() {
+            Some(Op::Elu(self.clone(), alpha))
+        } else {
+            None
+        };
+        Ok(from_storage(storage, self.shape(), op, false))
+    }
+
     fn check_dim(&self, dim: usize, op: &'static str) -> Result<()> {
         if dim >= self.dims().len() {
             Err(Error::DimOutOfRange {