The nonlinear elasticity and strain-tunable magnetocaloric effect (MCE) of antiferromagnetic monolayer MnPS₃ are demonstrated by multiscale modeling and simulations. A continuum constitutive model expanding the elastic strain energy density by a Taylor series is formulated to describe the nonlinear and large-deformation elasticity of monolayer MnPS₃. Fourteen independent elastic constants of the model are determined using the ab initio results. The nonlinear behavior is found to initiate at about 7% strain and nearly isotropic before the rupture. MCE (adiabatic temperature change ΔT and isothermal entropy change −ΔS) of monolayer MnPS3 is found anisotropic due to the anisotropy in the temperature derivative of magnetic susceptibility, i.e. stronger in-plane MCE. An in-plane biaxial strain could improve MCE by a factor of 1.5–2. The maximum  −ΔS and ΔToccur at around 10 K and are evaluated as 2.8 $\mathrm{<span\; style="font-family:"times\; new\; roman";font-size:18px;">\mu </span>}$J m−2 K−1 and 2.2 K, respectively, suggesting monolayer MnPS₃ as a potential candidate for low-temperature (¡ 20 K) magnetic refrigeration.