The ray method for solving dynamic boundary value problems for nonlinear thermo-elastic media, wherein heat propagates with a finite speed, is developed. By the action of initial and boundary conditions, two types of finite amplitude shock wave propagate in such media: quasi-thermal wave (fast wave) and quasi-longitudinal wave (slow wave). Behind the wave fronts the solution for the desired functions is constructed along the rays in terms of power series (ray series) whose coefficients are the discontinuities in various orders of partial derivatives of the functions to be found with respect to time, but a variable value is the time needed for a disturbance to propagate along the ray from the point under consideration up to the wave front; in so doing the power of the variable value corresponds to the order of the partial time-derivative of the desired function.