In this theses the frictionless contact problem between two- dimensional or three-dimensional deformable bodies with elasto-plastic behavior under finite strains is studied. The numeric solution procedure is based on an incremental- iterative strategy and includes the treatment of geometric and physical nonlinearities as well as those which arise from contact conditions. In the model of body the finite element method together with an updated Lagrangian and elasto-plastic constitutive relations for finite strains is used.For the solution of the contact problem two methods were investigated. The methods were the Penalty method, where the contact restritions are imposed in an aproximated manner with the use of a penalty parameter and the Linear Complementarity Programming method,which is based on the formulation of a mathematic programming problem for each configuration of equilibrium where the Kuhn-Tucker omplementarity conditions corresponding to the contact conditions are solved by the Lemke pivoting scheme [43]. A algorithm was implemented for consideration for the contact geometry where generic conditions of contact are assumed and the kinematic relation is expressed through a differentiable gap function.Displacement based elements with linear interpolations - hexahedral 8 node elements were employed for the space discretization. In order to diminish the locking effects present in these elements, a hibrid formulation - Enhanced Assumed Strain - EAS, with three aditional internal parameters of deformation with an complete trilinear deformation field was employed.