Besides the temperature and magnetic field, the strain and stress state of the superconducting Nb3Sn wires in multi-stage twisted cable-in-conduit conductors (CICCs), as applied in ITER or high field magnets, strongly influence their transport properties. For an accurate quantitative prediction of the performance and a proper understanding of the underlying phenomena, a detailed analysis of the strain distribution along all individual wires is required. For this, the thermal contraction of the different components and the huge electromagnetic forces imposing bending and contact deformation must be taken into account, following the complex strand pattern and mutual interaction by contacts from surrounding strands. In this paper, we describe a numerical model for a superconducting cable, which can simulate the strain and stress states of all single wires including interstrand contact force and associated deformation. The strands in the cable can be all similar (Nb3Sn/Cu) or with the inclusion of different strand materials for protection (Cu, Glidcop). The simulation results are essential for the analysis and conductor design optimization from cabling to final magnet operation conditions. Comparisons are presented concerning the influence of the sequential cable twist pitches and the inclusion of copper strands on the mechanical properties and thus on the eventual strain distribution in the Nb3Sn filaments when subjected to electromagnetic forces, axial force and twist moment. Recommendations are given for conductor design improvements.