The anisotropy induced through the calendering process was investigated in cyclic and monotonic uniaxial and biaxial tests monitored using an optical device. Thin sheets of Styrene-ethylene-co-butylene-styrene (SEBS) were extruded, which resulted in significant anisotropy in the polymer: the polymer chains are principally uniaxially oriented in the same direction as the calendering direction. Cyclic uniaxial tests reveal the Mullins effect and compressibility, which are higher in the calendering direction. A successful physically based hyper-elastic model is proposed, which includes anisotropic damage in the framework of continuum damage mechanics at large strains. Two sets of experimental data (samples cut in the calendering direction and in the transverse direction) are used to validate the constitutive model. Model parameters are estimated via scripts written in Matlab (R). Computational results agree rather well with experimental data, and highlight the influence of process on material properties. Model capabilities for predicting various test results (samples cut in the diagonal direction and tensile tests on a two-hole specimen) are critically discussed. (c) 2013 Elsevier Ltd. All rights reserved.