The Paper Shows Results of the Finite Element Modelling of Contact of a Rigid Spherical Body (indenter) with a Body from Elastic-Plastic Material. both the Proces of Loading and Unloading are Modelled. in Addition to Stresses, Also Energies are Investigated, Including their Distribution in the Plastically Deformed Core and the Elastically Deformed Outer Region. Attention is Devoted to Residual Stresses and Energies as well. Influence of Various Factors is Investigated, such as Various Values of Strain-Hardening Parameters (e.g. in Johnson-Cook Model), Relative Depth of Penetration (h/R), Coefficient of Friction.