X-ray diffraction is especially useful in analyzing the phase-transition response of thin-film SmS to strain impressed by the two-dimensional constraints of the substrate. A biaxial-stress model is applied and extended to a randomly-oriented crystalline film. The changes in macrostress, the compliance tensor and effective Poisson's ratio are evaluated near the hulk phase transition. An analysis of crystallite size and microstrain broadening is also presented including broadening effects due to biaxial macrostrain on the randomly-oriented crystallites. These results illustrate the effect of a constraining, biaxial-stress field on the unusual elastic character of samarium monosulfide. It is demonstrated that the thin-film geometry suppresses the first-order phase transition allowing only linear changes between the semiconducting and metallic states.