This paper first studies the transition matrix formulation for the analysis of responses of an elastic halfspace with a buried tunnel subjected to obliquely incident waves. The basis functions are constructed using the moving P-, SV-, and SH-wave source potentials and to represent the scattered and refracted wave fields in series forms. The associated T-matrix expression of elastic inclusion is derived using Betti's third identity. Second, this study proposes a technique for calculating the integral representation of basis functions in the wave-number domain using the method of steepest descent. Finally, typical numerical results obtained under incident plane waves are presented for verification.