It is difficult to establish a numerical model for a certain structure of electrospun nanofibrous mats, due to their high porosity and non-linear characteristics, that can fully consider these characteristics and describe their mechanical behaviors. In this paper, an analytical method of meso-mechanics was adopted to establish the tensile constitutive relationship between a single fiber and mats from fiber-web microstructures. Meanwhile, a macroscopic finite element model was developed and verified through uniaxial tensile stress-strain experimental data of silk fibroin (SF)/polycaprolactone (PCL) nanofibrous mats. The compared results show that the constitutive relation and finite element model could satisfactorily express elastic-plastic tensile mechanical behaviors of the polymer. This model helps regulate the microstructure of nanofibrous mats to meet the mechanical requirements in engineering applications.