This work presents a three dimensional elastic-plastic model for two hemispherical bodies sliding across one another under various preset vertical interferences. In particular, steel-on-steel and aluminum-on-copper contact situations are considered. A finite element analysis is used for the model and the parameters to investigate include stresses, deformations, contact areas, and energy loss in sliding. Both frictional and frictionless sliding are investigated. In addidition to structural loads, electromagnetic loads are considered and a framework for a electromagneticlly, structurally, and thermally coupled model is investigated.