Abstract The purpose of this paper is to study the numerical solution to the initialboundary value problem of the system of wave equations with heat conduction. Ten sets of boundary conditions are proposed, each of which can gUarantee the solution to be unique and stable. A difference scheme is constructed and a practical recursive algorithm is presented. The process of deriving the difference scheme is indirect, whose aim is for the theoretical anslysis of the deference scheme. It is proved by energy method that the scheme is uniquely solvable, unconditionally stable and second-order convergent. For the degenerate problem, similar results are also given.