Abstract: The existing analytical solutions to scattering of seismic waves are presented in the frequency domain and valid only in narrow frequency band, from which the reliable transient solution cannot be obtained. Addressing this problem, this paper used the broad-band frequency-rdomain analytical solution to obtain the broad-band frequency-esponse function for different spatial locations, and by Fourier transform, presented the analytical solution to the transient response of canyon topography SH wave incidence. Based on this, this paper studied the fundamental characteristics of transient response of canyon under the inputs of impulses and real ground motions, with the emphasis on the amplifying effect of the canyon on ground motion. This effect was defined by the ratio between the parameters, such as the peak and the spectral acceleration, etc., of seismic responses around the canyon, to those of seismic responses of free field, i.e. the elastic half-space. It was demonstrated that, under the impulse input, the displacement of the canyon corner was amplified distinctly, which was related to the impulse duration and the incident angle. As to the input of real ground motion, the spectral acceleration on the corner at the incident side of canyon is significantly amplified, with the maximum spectral ratio being as high as 2.0, which is related to the canyon geometries and the incident angle.