Young's modulus of tapered mixed composition (zinc-blende with a high density of twins and wurtzite with a high density of stacking faults) gallium phosphide (GaP) nanowires (NWs) was investigated by atomic force microscopy. Experimental measurements were performed by obtaining bending profiles of as-grown inclined GaP NWs deformed by applying a constant force to a series of NW surface locations at various distances from the NW/substrate interface. Numerical modeling of experimental data on bending profiles was done by applying Euler-Bernoulli beam theory. Measurements of the nano-local stiffness at different distances from the NW/substrate interface revealed NWs with a non-ideal mechanical fixation at the NW/substrate interface. Analysis of the NWs with ideally fixed base resulted in experimentally measured Young's modulus of 155 +/- 20 GPa for ZB NWs, and 157 +/- 20 GPa for WZ NWs, respectively, which are in consistence with a theoretically predicted bulk value of 167 GPa. Thus, impacts of the crystal structure (WZ/ZB) and crystal defects on Young's modulus of GaP NWs were found to be negligible.