In the statistical theory of damage, the following functional equation plays a role: μ(x) = ∫ x 0 K(x,y)[μ(y) + μ(x−y−1)]dy, x > 0, where the kernel K is a positive and twice continuously differentiable function for 0 < y ≤ x with the property that ∫ x 0 K(x,y)dy = 1,x > 0. The unknown function satisfies the following initial conditions: μ(χ) = 0, χ < 0, μ(χ) = 1, 0 ≤ x ≤ 1. This functional equation gives rise to many analytical solutions using Tauberian theorems. In addition to these solutions, we intend to show the numerical aspect of the problem. We will study the boundary and the asymptotic behavior of μ(χ)w for a given class of kernels μ(x) = 0, x < 0, μ(x) = 1, 0 ⩽ x ⩽ 1. as well as the approximation of μ(χ) for small values of χ using cubic cardinal spline functions. Numerical examples are given to illustrate the method and to define the shape of the distribution of damage for special cross-sections.