Considerable attention has been paid to the bimaterial thermostat stress analysis problem as regards applications in microelectronic packaging. When a bimaterial beam is subjected to a temperature change, internal stress is developed that generates curvature. The present paper generalizes previous idealizations whereby a linear elastic material response has been assumed. We treat each of the beam materials as elastic-plastic with a bilinear response. A solution is obtained for the stress and deformation in the bimaterial structure following a “strength of materials” approach. While the solution is imperfect in that the stress free boundary conditions at the ends of the strip are not satisfied exactly, it does capture the overall behavior of the bimaterial beam but for the well-known end effect. Several numerical examples are presented using design data for materials commonly encountered in microelectronics applications.