The contribution at hand aims to numerically simulate the nail driving process using the finite element method. The geometrical constraint of the impenetrability between the surfaces of the two contacting bodies is delivered using a displacement-driven approach. The Coulomb friction law is employed to describe the interaction between two contacting surfaces, where the coefficient of friction is obtained experimentally. In this work, the driving of a nail into blocks of polyurethane (PUR) and spruce wood is simulated in a quasi-static manner. Von Mises plasticity is employed to model PUR, while a more complicated constitutive model is utilized for spruce wood. This constitutive formulation considers the influence of the grain direction as well as the nonlinear behavior of spruce wood. The driving forces obtained from the numerical simulation are compared to the experiments. Despite simplifications and assumptions, the comparison demonstrates reasonable agreement in the simulation of nailing into PUR. Under the same circumstances, the comparison in the case of spruce wood shows a more reasonable agreement at the initial stages but fails prematurely due to severe mesh distortion. Overlooking the distortion issue, which must be further investigated, the outcome demonstrates the stability and reliability of the material and contact model.