As part of the study of the nonlinear response of structural components we investigate in this report a single degree-of-freedom nonlinear response equation usually known as Duffing's equation. Previously the response curves have been investigated analytically by many authors but there seems to have been very little numerical work done in the nonlinear cases. It is shown that a numerical solution is feasible and that some of the standard analytical approximations are not accurate in the peak region of the response curve.