Soft tissues are pseudoelastic anisotropic materials; various formulas for their strain energy density have been proposed for modelling of their constitutive behaviour. However, the individual variance of elastic parameters is often more pronounced than their anisotropy, so that their constitutive relations can be modelled as either isotropic or orthotropic. Any hyperelastic model requires more mechanical tests to be input for an identification of its parameters than mere uniaxial tension tests; especially biaxial tension tests are very important also for isotropic hyperelastic materials. A design of a testing rig produced in cooperation of our institute with some local companies is presented. It enables us to carry out not only equibiaxial tension tests, but also some other biaxial tensile tests, because displacements in both mutually perpendicular directions can be controlled independently. The proposal of various types of biaxial tests is presented in the paper, with examples of their realization with porcine aortic wall tissue. The contribution focuses on ways of evaluation of the results and on identification of parameters of various constitutive models. The use of more mechanical tests in identification of constitutive parameters can improve the predictive capability of the models substantially.