A numerical study is made of the one-dimensional transient, uncoupled dynamic thermal stresses in plane, cylindrical, and spherical bodies subjected to a step change in temperature on its internal boundary. The numerical procedure employs the characteristic relations on boundaries and on interfaces between media with different material properties while using an explicit finite-difference scheme at all other points. Fundamental problems with and without external boundaries are solved, and the results show clearly the propagation and reflection of discontinuities in stresses and velocity due to a step heating on the internal boundary. The solutions of the specific examples calculated show excellent agreement with existing solutions by other methods. Numerical results are also given for the stress wave propagation in laminated media consisting of two layers with different material properties.