Mechanical testing and modelling of a material for biomedical applications have to be based on conditions representative of the application of interest. In this work, an ether-based polyurethane elastomer is used to build mock arteries. The aim is to study the behaviour of arteries under pulsatile loading conditions and how that behaviour changes with the development and progression of atherosclerosis. Polyurethane elastomers are widely used as biomaterials, e.g. in tube form for bypasses and catheters. However, their mechanical behaviour has not been extensively characterised. This work establishes the variations in the behaviour of polyurethane elastomer with temperature, humidity and strain rate and also reports planar and equibiaxial tension, relaxation, creep and cyclic test results, providing a comprehensive characterisation of the material. Test results are used to determine the properties of the polyurethane elastomer and in the selection of a representative material model for future simulations of arterial behaviour and the development of atherosclerosis. The results show that the behaviour of the elastomer is significantly dependent on both humidity and temperature, with Young's modulus of 7.4 MPa, 5.3 MPa and 4.7 MPa under dry-room temperature, wet-room temperature and wet at 37 ( composite function)C conditions, respectively. The elastomer also exhibits rate-dependent viscoelastic behaviour. Yeoh's hyperelastic material model provided the best fit to the entire range of experimental data. The Neo-Hookean model provides a good fit at small strain but significantly diverges at large strains. Nevertheless, in applications where deformations are relatively small, i.e. below 15%, the Neo-Hookean model can be used.