Experimental mechanical studies require a reliable transfer of the desired load to the test sample. The design of advanced mechanical grips implies numerical calculations of experimental testing with the aim of improving the test method. In this thesis, a numerical analysis of the multiaxial Arcan rigs was performed. Furthermore, the geometry of the corresponding butterfly test sample was optimized. The aim of this work is to imitate mechanical experiment via numerical simulations in order to verify the stiffness of mechanical rigs and to ensure that reliable multiaxial loading is applied during the real experimental investigation. The topic of this thesis considers multiaxial grips that can impose different biaxial loading regimes. Hence, displacement fluctuations were measured on the butterfly sample with numerical calculations during tensile, shear and their combination when the sample is loaded with under 45°. The theoretical displacement distribution was studied on the idealized test sample with the appropriate boundary conditions. Consequently, the results obtained from idealized test case were compared with the results captured by the numerical experiment analysis. As a part of the finite element method application, various verification examples were performed in order to estimate the accuracy of the prescribed finite elements, boundary conditions, loading modes and the contact method. Within this thesis, the geometry of the butterfly test sample was also optimized using the sensitivity field. Behavior of the sample material is described with elastoplastic constitutive law, taking into account the Armstrong-Frederick's kinematic hardening. The developed iterative algorithm is used to optimize two characteristic dimensions of the sample (radius R and angle α) that define two symmetric V notch. By increasing the displacement sensitivity field and the force sensitivity vector of the proposed test sample, optimal dimensions for the three stress plane states were determined.