Future high-field magnets for particle accelerators hinge on the crucial development of advanced Nb₃Sn wires engineered to withstand the large stresses generated during magnet assembly and operation. The superconducting properties of Nb₃Sn enable the design of compact accelerator-quality magnets above 10 T, but at the same time the brittleness and strain sensitivity of the material impose careful consideration of the mechanical limits. In addition, accelerator magnets are wound using Rutherford cables and the cabling process generates deformations in the wire that can affect its electro-mechanical performance. This paper reports on the impact of the rolling deformation on the transverse stress tolerance of high-performance restacked-rod-process (RRP^®) and powder-in-tube (PIT) Nb₃Sn wires. Rolling deformation was used to mimic the effect of cabling on the wire shape. Deformed samples were compared to reference round wires in term of stress dependence and irreversible limit (σ_irr) of the critical current (I_c) under transverse compressive loads up to 240 MPa. Experiments were performed at 4.2 K, 19 T, on resin-impregnated single wires that imitate the operating conditions in a Rutherford cable of an accelerator magnet. The results show that rolling deformation has a detrimental effect on the initial I_c of PIT wires, but it does not influence the behavior of the wire under stresses above 70 MPa. On the other hand, the deformation of RRP^® wires leads to an improved σ_irr without affecting the initial I_c. Additionally, a 2D-mechanical finite element method model of the RRP^® wire was developed to investigate the impact of the wire geometry on the plastic deformation of the copper matrix, which induces residual stresses on Nb₃Sn and is the main cause for the permanent reduction of I_c. Based on the model results, an alternative layout of the wire was proposed that improves its stress tolerance without affecting its electrical transport properties.