Future particle colliders in search for new physics at the energy frontier require the development of accelerator magnets capable of producing fields well beyond those attainable with Nb-Ti. As the next generation of high-field accelerator magnets is presently planned to be based on Nb ₃ Sn, it becomes crucial to establish precisely the mechanical limits at which this brittle and strain sensitive superconductor can operate safely. This paper reports on the stress dependence and the permanent reduction of the critical current under transverse compressive loads up to 240 MPa in state-of-the-art restacked-rod-process (RRP ^® ) and powder-in-tube Nb ₃ Sn wires. Single-wire experiments were performed at 4.2 K in magnetic fields ranging between 16 T and 19 T on resin-impregnated samples to imitate the operating conditions of a wire in the Rutherford cable of an accelerator magnet. Depending on the wire technology, we measured irreversible stress limit values—defined as the transverse stress value, leading to a permanent reduction in the critical current of 5%, assessed by convention at 19 T—ranging between 110 MPa and 175 MPa. This permanent reduction of the critical current after mechanical unload can occur for two reasons, which can be concomitant: the plastic deformation of the Cu matrix that produces residual stresses on the Nb ₃ Sn lattice and the formation of cracks. We developed a method to identify the dominant degradation mechanism in our experiments that allowed us to predict the fraction of critical current lost due to residual stresses. Interestingly, we found that in the RRP ^® wires the measured reduction of I _c after unload from stresses as high as 240 MPa can be fully ascribed to residual stresses. An independent confirmation of this conclusion coming from a study combining x-ray tomography and deep learning Convolutional Neural Networks is also reported.