The seismic response of a sedimentary basin is especially important since many highly populated areas are located on them. The frequency responses at ground surface of the two-dimensional semi-circular basin under the incident SH-, P- and SV- waves are obtained by using the indirect boundary integral equation method. Three different incident angles (0¢X, 30¢X and 60¢X) are employed in this study, while three different impedance contrast models are used in the vertical incident SH case. With an alteration in the incident angle of all waves, the amplitude and the fundamental frequency are changed accordingly. The empirical formula for the fundamental frequencies predicted by Bard and Bouchon (1985) can fit the results calculated from this semi-circular basin model at around the basin center. The transient response is constructed from the steady state solution by the Fourier synthesis. The authors use Ricker wavelets as the incident wave with three different characteristic periods (10, 5 and 3.3 in dimensionless units) to analyze the effects on the peak value and duration time. The results show the amplification effects of the peak value are very significant on the top of the basin area. The greater the impedance contrast, the more amplified the peak is, and the larger is the duration. The wavelength and incident angle of the input motion also have strong effects on the peak ground motion and duration time.