In this manuscript, we present the study of elastic properties of InP nanowires with help of scanning probe microscope in advanced PeakForce Tapping® regime. The measuring method was developed in order to investigate the Young's modulus of these cone-shaped structures with significant accuracy. The difference in InP elasticity for wurtzite phase and zinc- blende phase was revealed. It was shown that elastic modulus of InP nanowires significantly increases from 60 GPa to more than 100 GPa when diameter of a nanowire is reduced below 50 nm. The core-shell model for InP nanowire was used for the explanation of this effect.