We propose a comprehensive description of the strain configuration induced by the lattice mismatch in a core-shell nanowire with circular cross-section, taking into account the crystal anisotropy and the difference in stiffness constants of the two materials. We use an analytical approach which fully exploits the symmetry properties of the system. Explicit formulae are given for nanowires with the wurtzite structure or the zinc-blende structure with the hexagonal/trigonal axis along the nanowire, and the results are compared to available numerical calculations and experimental data on nanowires made of different III–V and II–VI semiconductors. The method is also applied to multishell nanowires, and to core-shell nanowires grown along the 〈0 0 1〉 axis of cubic semiconductors. It can be extended to other orientations and other crystal structures.