Electro-spun biodegradable polymer fibrous structures exhibit anisotropic mechanical properties dependent on the degree of fibre alignment. Degradation and mechanical anisotropy need to be captured in a constitutive formulation when computational modelling is used in the development and design optimisation of such scaffolds. Biodegradable polyester-urethane scaffolds were electro-spun and underwent uniaxial tensile testing in and transverse to the direction of predominant fibre alignment before and after in vitro degradation of up to 28 days. A microstructurally-based transversely isotropic hyperelastic continuum constitutive formulation was developed and its parameters were identified from the experimental stress-strain data of the scaffolds at various stages of degradation. During scaffold degradation, maximum stress and strain in circumferential direction decreased from 1.02±0.23 MPa to 0.38±0.004 MPa and from 46±11% to 12±2%, respectively. In longitudinal direction, maximum stress and strain decreased from 0.071±0.016 MPa to 0.010±0.007 MPa and from 69±24% to 8±2%, respectively. The constitutive parameters were identified for both directions of the non-degraded and degraded scaffold for strain range varying between 0% and 16% with coefficients of determination r 2 > 0.871. The six-parameter constitutive formulation proved versatile enough to capture the varying non-linear transversely isotropic behaviour of the fibrous scaffold throughout various stages of degradation.