Abstract This article presents the application of the Finite Element Method (FEM) for estimating the penerration resistance and the stress and strain state in the soil around a penetrating rod. Numerical solutions are obtained assuming Lagrangian formulation with finite deformations. The Jauman terms are incorporated in the analysis. A constitutive law by Kolymbas is used. A condition representing skin friction has been defined for the surfce of the penetrometer, and subsequently the unknown stress state on its surface is determined with an iterative method. The method is closely connected with the localization of deformation. Some numerical problems due to time-integration and convergence criteria for incrementally nonlinear constitutive laws are also discussed. In numerical computations, the friction coefficient parameter is varied. The influence of this parameter on the penetration resistance is discussed.