Electrospinning is a promising technology to produce scaffolds for cardiovascular tissue engineering. Each electrospun scaffold is characterized by a complex micro-scale structure that is responsible for its macroscopic mechanical behavior. In this study, we focus on the development and the validation of a computational micro-scale model that takes into account the structural features of the electrospun material, and is suitable for studying the multi-scale scaffold mechanics. We show that the computational tool developed is able to describe and predict the mechanical behavior of electrospun scaffolds characterized by different microstructures. Moreover, we explore the global mechanical properties of valve-shaped scaffolds with different microstructural features, and compare the deformation of these scaffolds when submitted to diastolic pressures with a tissue engineered and a native valve. It is shown that a pronounced degree of anisotropy is necessary to reproduce the deformation patterns observed in the native heart valve.