The contact between piston-ring and cylinder-bore is generally nonuniform, due to mechanical and thermal distortion of the bore and manufacturing imperfection in the shape of the free ring. This nonuniform contact problem is treated in the present work that features arbitrarily specified bore shape and free ring shape, and also includes the thermal deformation of the ring and the effect of gas pressure. The problem is solved with the elastica theory, incorporating thermal elasticity, and a complementarity formulation. Solutions are computed using dimensions, material values, and operating parameters representative of those found in automotive engines.