The seismic ground motions are studied in an infinite half-space with a non-circular alluvial valley under time harmonic incident anti-plane shear waves. Based on the conformal mapping method and Fourier series expansions, the conditions of displacement continuity and stress equilibrium at the interface of alluvial valley are set as semi-circular alluvial valley in conformal plane, then the result is obtained by constructing a set of infinite linear algebraic equations with boundary discretization. The unknown coefficients in the algebraic system can be easily determined. The present method is treated as a semi-analytical solution since error only attributes to the truncation of Fourier series. Earthquake analysis for the site response of alluvial valley or canyon subject to the incident SH-wave is the main concern. Numerical examples for semi-elliptic alluvial valley are given to test our program. The research indicates that great interaction exists between the alluvial valley and the horizontal surface, which will bring on great influence on ground motion. Therefore enough importance must be attached to the existing of subsurface cavity while finishing seismic design.