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The effect of sidewall nucleation on nanowire morphology is studied theoretically. The model provides a semiquantitative description of nanowire radius as a function of its length and the distance from the surface. It is demonstrated that the wire shape critically depends on the diffusion flux of adatoms from the substrate and on the rate of direct impingement to the sidewalls. At high diffusion flux the wire shape is cylindrical. A decrease of diffusion from the surface leads to the onset of nucleation on the sidewalls resulting in the lateral extension and in the reduction of wire length. The wire shape changes from cylindrical to conical, because the supersaturation of adatoms driving the nucleation is higher at the wire foot than at the top. It is shown that the shape modification becomes pronounced at low growth temperatures. Theoretical results are used to model the experimentally observed shapes of GaAs and GaP wires, grown by Au-assisted molecular beam epitaxy at different temperatures.