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A class of nonlocal nonlinear wave equation arises from the modeling of a onedimensional motion in a nonlinearly, nonlocally elastic medium. The equationinvolves a kernel function with nonnegative Fourier transform. We discretizethe equation by using Fourier spectral method in space and we prove theconvergence of the semidiscrete scheme. We then use a fully-discrete scheme,that couples Fourier pseudo-spectral method in space and 4th order Runge-Kuttain time, to observe the effect of the kernel function on solutions. To generatesolitary wave solutions numerically, we use the Petviashvili's iterationmethod.

Numerical solution for a general class of nonlocal nonlinear wave equations