One of the strength problems for modern structural materials is the mathematical design of components made from shape-memory alloys (SMA), among which the most commonly encountered examples are unions for thermomechanical pipeline joints [1]. In this paper we discuss a numerical solution obtained for a connected axisymmetric direct-transformation boundary-value problem by a procedure based on new determining equations for deformable solids that undergo thermoelastic martensitic transformations. The results reported below may be useful not only for theoretical investigation of processes in solid bodies made from SMA, but also for modeling of the effects that arise in the pipe unions during service.