Recent independent experiments demonstrated that the lithiation-induced volume expansion in silicon nanowires, nanopillars, and microslabs is highly anisotropic, with predominant expansion along the <110> direction but negligibly small expansion along the <111> direction. The origin of such anisotropic behavior remains elusive. Here, we develop a chemomechanical model to study the phase evolution and morphological changes in lithiated silicon nanowires. The model couples the diffusive reaction of lithium with the lithiation-induced elasto-plastic deformation. We show that the apparent anisotropic swelling is critically controlled by the orientation-dependent mobility of the core-shell interface, i.e., the lithiation reaction rate at the atomically sharp phase boundary between the crystalline core and the amorphous shell. Our results also underscore the importance of structural relaxation by plastic flow behind the moving phase boundary, which is essential to quantitative prediction of the experimentally observed morphologies of lithiated silicon nanowires. The study sheds light on the lithiation-mediated failure in nanowire-based electrodes, and the modeling framework provides a basis for simulating the morphological evolution, stress generation, and fracture in high-capacity electrodes for the next-generation lithium-ion batteries.