diff --git a/src/scalar.jl b/src/scalar.jl
index 093a36d..424539e 100644
--- a/src/scalar.jl
+++ b/src/scalar.jl
@@ -154,6 +154,23 @@ inverse_eltype(::TVNeg, ::Type{T}) where T = typeof(-oneunit(T))
 inverse(::TVNeg, x::Number) = -x
 inverse_and_logjac(::TVNeg, x::Number) = -x, logjac_zero(LogJac(), typeof(x))
 
+"""
+$(TYPEDEF)
+
+“Softplus” transformation `x ↦ log(1+exp(x))`.
+
+!!! NOTE
+    This is *experimental* and not part of the API yet.
+"""
+struct TVSoftPlus <: ScalarTransform end
+
+transform(::TVSoftPlus, x::Real) = log1pexp(x)
+transform_and_logjac(t::TVSoftPlus, x::Real) = transform(t, x), -log1pexp(-x)
+
+inverse_eltype(::TVSoftPlus, ::Type{T}) where T = _ensure_float(T)
+inverse(::TVSoftPlus, y::Number) = logexpm1(y)
+inverse_and_logjac(::TVSoftPlus, y::Number) = logexpm1(y), -log1mexp(-y)
+
 ####
 #### composite scalar transforms
 ####
diff --git a/test/runtests.jl b/test/runtests.jl
index fa352f9..326a4a3 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -986,6 +986,10 @@ end
     @test_throws InexactError inverse(t, fill(Complex(0, 1), 3))
 end
 
+@testset "TVSoftPlus" begin
+    test_transformation(TransformVariables.TVSoftPlus(), y -> y > 0)
+end
+
 ####
 #### static analysis with JET
 ####