Due to their unique boundary conditions, nanowire heterostructures may exhibit defect-free interfaces even for systems with large lattice mismatch. Heteroepitaxial material integration is limited by lattice mismatches in planar systems, but we use a variational approach to show that nanowire heterostructures are more effective at relieving mismatch strain coherently. This is an equilibrium model based on the Matthews critical thickness in which the lattice mismatch strain is shared by the nanowire overlayer and underlayer, and could as well be partially accomodated by the introduction of a pair of misfit dislocations. The model is highly portable to other nanowire material systems and can be used to estimate critical feature sizes. We find that the critical radius of this system is roughly an order of magnitude larger than the critical thickness of the corresponding thin film/substrate material system. Finite element analysis is used to assess some aspects of the model; in particular, to show that the variational approach describes well the decay of the strain energy density away from the interface.