In this research, copper chromite (CuCr2O4) nanoparticles (NPs) were synthesized by the sol–gel auto‐combustion method. The effects of CuCr2O4 NPs and polyurethane (PU) on the tensile strength of the epoxy (EP) resin were studied by considering different weight percentages (wt%). The response surface methodology (RSM) coupled with central composite design (CCD) (RSM/CCD) methods were also used to optimize the Young's modulus, yield strength, and ultimate tensile strength of the EP/PU/CuCr2O4 nanocomposites. The composition structure and morphology of the EP/PU/CuCr2O4 nanocomposites were determined using the Fourier Transform Infrared spectroscopy (FT‐IR), X‐ray diffraction, UV–vis diffuse reflection, Scanning Electron Microscopy, X‐ray energy dispersive spectroscopy, and thermogravimetric analysis. It was also shown that the RSM/CCD methods could be utilized effectively to find the optimum process variables in the tensile test of the EP/PU/CuCr2O4 nanocomposites. Moreover, the tensile test revealed that the presence of the CuCr2O4 NPs in the EP/PU matrix improved the mechanical properties. Best results were obtained with the 0.76 wt% of the CuCr2O4 NPs and the 2.6 wt% PU in the epoxy resin. The molecular dynamic simulation was used to illustrate the effect of the NPs on the interaction energy and mechanical properties of this nanocomposite. The calculated interaction energy for the EP/PU/CuCr2O4 nanocomposites was −437.96 Kcal/mol. The results showed that Young's modulus had relative agreement with the experimental results.