The mechanical properties of biomaterial scaffolds are crucial for their efficacy in tissue engineering and regenerative medicine. At the microscopic scale, the scaffold must be sufficiently rigid to support cell adhesion, spreading, and normal extracellular matrix deposition. Concurrently, at the macroscopic scale the scaffold must have mechanical properties that closely match those of the target tissue. The achievement of both goals may be possible by careful control of the scaffold architecture. Recently, electrospinning has emerged as an attractive means to form fused fibre scaffolds for tissue engineering. The diameter and relative orientation of fibres affect cell behaviour, but their impact on the tensile properties of the scaffolds has not been rigorously characterized. To examine the structure-property relationship, electrospun meshes were made from a polyurethane elastomer with different fibre diameters and orientations and mechanically tested to determine the dependence of the elastic modulus on the mesh architecture. Concurrently, a multiscale modelling strategy developed for type I collagen networks was employed to predict the mechanical behaviour of the polyurethane meshes. Experimentally, the measured elastic modulus of the meshes varied from 0.56 to 3.0 MPa depending on fibre diameter and the degree of fibre alignment. Model predictions for tensile loading parallel to fibre orientation agreed well with experimental measurements for a wide range of conditions when a fitted fibre modulus of 18 MPa was used. Although the model predictions were less accurate in transverse loading of anisotropic samples, these results indicate that computational modelling can assist in design of electrospun artificial tissue scaffolds.