To evaluate the mechanical properties of anisotropic materials it is necessary to use biaxial testing test during which data on stress and deformations are measured in two directions. Biaxial tensile testing is performed on devices called tensile testing machines. In practice, this type of testing is most often used to test the properties of biomaterials such as arterial tissue or to test different composite materials. Since the samples of biomaterials are small in size, we should pay attention to the choice of the type of sample acceptance with the aim of achieving greater homogeneity of the stress and deformation field. The most commonly used sample acceptance is in the form of clamping jaws whose contact with the specimen is based on the coefficient of friction. In this paper, five coefficients of friction at contact between clamping jaws and five different types of samples were experimentally determined. With the known maximum stretching force and coefficient of friction, the value of normal force was determined which was used as input data for the numerical simulation, which was carried out using finite element method. The aim of this simulation was to verify the strength and stiffness of the clamping jaws during maximum load. Also, a numerical analysis of five different hyperelastic materials in theoretical and real case is presented. In the theoretical case, the sample is loaded only by tensile forces, while in the real case, the action of force of tightening the clamping jaws is also taken into account. The aim of this simulation was to analyze the influence of the tightening force on the homogeneity of the stress field and to determine the approximately required tightening torque. If the tightening torque is too high, the sample is unnecessarily deformed when placed on the device and the stress concentration increases. On the other hand, if the tightening torque is too small, the sample may slip during the experiment and the experiment is then unsuccessful. The SolidWorks software package was used to create the model, while numerical analyzes were performed in the Abaqus software package.