Controlling nanomaterial shape beyond its basic dimensionality is a concurrent challenge tackled by several growth and processing avenues. One of these is strain engineering of nanowires, implemented through the growth of asymmetrical heterostructures. Here, we report metal-organic molecular beam epitaxy of bent InP/InAs core/shell nanowires brought by precursor flow directionality in the growth chamber. We observe the increase of bending with decreased core diameter. We further analyze the composition of a single nanowire and show through supporting finite element simulations that strain accommodation following the lattice mismatch between InP and InAs dominates nanowire bending. The simulations show the interplay between material composition, shell thickness, and tapering in determining the bending. The simulation results are in good agreement with the experimental bending curvature, reproducing the radius of 4.3 µm (±10%), for the 2.3 µm long nanowire. The InP core of the bent heterostructure was found to be compressed at about 2%. This report provides evidence of shape control and strain engineering in nanostructures, specifically through the exchange of group-V materials in III-V nanowire growth.