Lorentz force is applied to coil windings when the magnet is charged. The coil windings are subjected to huge hoop tensile stress and transverse compressive stress in both the radial and axial directions due to the Lorentz force. The higher the magnetic field and the larger the bore, the larger the Lorentz force applied to the coil windings. Thus, not only the hoop stress, but also transverse compressive stress should be taken into account when designing the magnet. In this paper, we focus on transverse compressive stress, and the influence of this stress on critical current is explored for a standard Nb₃Sn wire and a Cu-NbTi-reinforced Nb₃Sn wire. It was confirmed that Cu-NbTi sufficiently reinforced the superconducting wire, not only for tensile stress, but also for transverse compressive stress. The effect of reinforcement arrangement in the cross section was also investigated. In the case that Cu-NbTi reinforcement is arranged at the center of the wire, there was less deterioration in superconducting property than in the case of the reinforcement being arranged in the outer part of the wire.