We considered a polycrystalline cylindrical nanowire with bamboo microstructure strained uniaxially by an external load. Our molecular dynamic computer simulations demonstrated that grain boundary grooving plays an important role in determining the morphological stability of nanowires. Also, an exceptionally high yield stress of nanowires emphasizes the importance of diffusion in their plastic deformation under applied load. We formulated a phenomenological diffusion-based model describing morphological stability and diffusion-controlled deformation behaviour of polycrystalline nanowires. The kinetics of the shape changes was calculated numerically.