Critical dimensions for nanowire core-multishell heterostructures are analyzed by using finite-element method based on the energy equilibrium criteria. Results show that the nanowire core-shell heterostructure can sufficiently reduce the strain in the shell and increase the critical shell thickness. The critical dimensions for the nanowire core-multishell heterostructure are determined by the stress fields generated at two heterointerfaces. For thin barrier, the critical dimensions decrease as the core radius increases, while when the barrier is thick enough, the critical dimensions show an increase with the increase of core radius conversely. This can be attributed to a competition between the lattice mismatch and strain distribution, which dominate the critical dimensions alternatively. Two critical quantum well thicknesses are obtained in the nanowire core-multishell heterostructure. Below the dislocation-free critical thickness, the structure will be coherent regardless of the barrier thickness. While above the dislocation-unavoidable thickness, dislocations are always energetically favored. In the dislocation-controllable region between the two critical thicknesses, coherent structure can be obtained via controlling the well and barrier thicknesses. The results are in good agreement with the experimental data and may serve as guidance for the design of coherent nanowire core-multishell quantum well structures and devices.