Acoustic streaming is one of the nonlinear phenomena produced by strong sound waves. This type of streaming is driven by acoustic momentum flux in an attenuating sound field. A strong standing wave in a duct generated by finite-amplitude oscillation of the air column dissipating due to friction at the duct wall produces acoustic streaming. The velocity of streaming is estimated from the steady part of the second-order term of a perturbation expansion of a sinusoidal oscillation. However, finite-amplitude oscillation gives rise to shock-wave propagation in the duct. In order to estimate acoustic streaming produced by finite-amplitude oscillation, it is necessary to analyze the response of the oscillatory boundary layer to shock waves in detail. The present paper deals with numerical analysis of the acoustic streaming described above. The fourth-order spatial difference method is applied to two-dimensional analysis of acoustic streaming in this work. Calculated results show velocity distributions in the oscillatory boundary layer and structures of steady streaming for various amplitudes of oscillation.