A new numerical procedure called asymptotic periodic waveform evaluation (APWE) for finding the steady state solution of nonlinear circuits driven by one tone periodic input signal is presented. APWE starts by constructing a virtual system which gives the same periodic steady state waveform as the original system's but with a shorter transient duration. Thus the periodic steady state (PSS) response can be obtained by simply performing transient analysis of the newly derived system for a few periods. An efficient method for solving the nonlinear equations occurred during the transient analysis is presented. To improve the convergence rate of PSS waveform, APWE is combined with extrapolation method. Some simulation results are shown.