We compute strain distributions in core-shell nanowires of zinc blende structure. We use both continuum elasticity theory and an atomistic model, and consider both finite and infinite wires. The atomistic valence force-field (VFF) model has only few assumptions. But it is less computationally efficient than the finite-element (FE) continuum elasticity model. The generic properties of the strain distributions in core-shell nanowires obtained based on the two models agree well. This agreement indicates that although the calculations based on the VFF model are computationally feasible in many cases, the continuum elasticity theory suffices to describe the strain distributions in large core-shell nanowire structures. We find that the obtained strain distributions for infinite wires are excellent approximations to the strain distributions in finite wires, except in the regions close to the ends. Thus, our most computationally efficient model, the FE continuum elasticity model developed for infinite wires, is sufficient, unless edge effects are important. We give a comprehensive discussion of strain profiles. We find that the hydrostatic strain in the core is dominated by the axial strain-component, ε_ZZ . We also find that although the individual strain components have a complex structure, the hydrostatic strain shows a much simpler structure. All in-plane strain components are of similar magnitude. The nonplanar off-diagonal strain components ( ε_XZ and ε_YZ ) are small but nonvanishing. Thus the material is not only stretched and compressed but also warped. The models used can be extended for the study of wurtzite nanowire structures, as well as nanowires with multiple shells.