A modified Landau-Ginzburg-Devonshire phenomenological thermodynamic theory is used to investigate both the influence of biaxial compressive misfit strain between film and the substrate and the mechanical stress on the multicaloric response in epitaxial EuTiO3 thin films. The complicated compressive misfit strain-temperature phase diagram in the low-temperature region is developed. The excellent electrocaloric and elastocaloric effect can be achieved: Delta T(TC)=3.66K, while Delta E=100kV/cm,um=-4.0%; Delta T = 5.31 K at 200 MPa. Besides, the maximal adiabatic temperature change Delta T(TM)=17.3K, while Delta H=5T,um=-4.0%, in the low-temperature region, which is comparable with the experimental result. Both the misfit strain and the external mechanical stress play a crucial role in the multicaloric response in EuTiO3 films. It may open more opportunities for practical application in refrigeration devices, especially for low-temperature solid-state multicaloric cooling.