A 3D numerical modelling technique for solving problems involving superconducting materials is presented. The model is implemented in finite element method software and is based on a recently developed 3D formulation for general electro-magnetic problems with solid conductors. It has been adapted for modelling of superconductors with non-linear resistivity in 3D, characterized by a power-law E-J relation. It has firstly been compared with an existing and verified 2D model: compared are the current density distribution inside the conductors and the self-field ac losses for different applied transport currents. Secondly, the model has been tested for computing the current distribution with typical 3D geometries, such as corner-shaped and twisted superconductors. Finally, it has been used with two superconducting filaments in the presence of external magnetic field for verifying the existence of coupling currents. This effect deals with the finite length of the conductors and cannot be taken into account by 2D models.