The seismic analysis of a viscoelastic half-space under two-dimensional (2D) oblique incident waves is carried out by the finite/infinite element method (FIEM). First, the frequency-domain exact solutions for the displacements and stresses of the free field are derived in general form for arbitrary incident P and SV waves. With the present formulation, no distinction needs to be made for SV waves with over-critical incident angles that make the reflected P waves disappear, while no critical angle exists for P waves. Next, the equivalent seismic forces of the earthquake (Taft Earthquake 1952) imposed on the near-field boundary are generated by combining the solutions for unit ground accelerations with the earthquake spectrum. Based on the asymmetric finite/infinite element model, the frequency-domain motion equations for seismic analysis are presented with the key parameters selected. The results obtained in frequency and time domain are verified against those of Wolf’s, Luco and de Barros’ and for inversely computed ground motions. The parametric study indicated that distinct phase difference exists between the horizontal and vertical responses for SV waves with over-critical incident angles, but not for under-critical incident angles. Other observations were also made for the numerical results inside the text.