<p>Due to the high critical current density <i>J</i>_c, Nb₃Sn becomes the promising candidate for future high-field magnets. Unfortunately, especially at high fields, mechanical loads such as Lorentz force and thermal stress can lead to damages, critical property degradations, and even quench. It has long plagued high-<i>J</i>_c Nb₃Sn wire at the core of high-field magnets, and seriously threaten applications of Nb₃Sn magnets. In this paper, we introduce a multiscale nonlinear mechanical model coupled with progressive damage effects, thermal, and electromagnetic fields to simulate the multi-physics behaviors of superconducting magnets. This model is validated by conducting comparisons with uniaxial tensile experiments of multi-filamentary Nb₃Sn wires and further measurements conducted on Nb₃Sn solenoid magnets. Leveraging this model, we investigate the nonlinear mechanical response of Nb₃Sn solenoid during preloading, cooling down, and current ramping process. There exist obvious mechanical property deteriorations caused by filament damages and plastic deformation of Copper matrix at high fields. Remarkably, mechanical reaction results in significant degradation of quench current threshold, and changes the quench propagation path. The current margin of Nb₃Sn solenoid of FECR (first 4th generation electron cyclotron resonance ion source) magnet versus transport current with consideration of strain sensitivities of <i>J</i>_c has been illustrated. These findings pave the way for analysis of elastoplastic damage behaviors and quench characteristics of superconducting solenoid magnet wounded by multi-filamentary wires.</p>