In this work, two nucleon-nucleon potentials were used to calculate the elastic collision reaction of two alpha-alpha particles with the formation of a short-lived ⁸Be nucleus within the framework of the cluster model. Together with them, the cluster model method was used in the calculations, which became a powerful tool for theoretical analysis and solution of this problem. One such model is the microscopic cluster model, or the method known as the algebraic version of the resonating group method (ARGM), which will allow us to explore this problem from a new angle and obtain data on resonant states. The advantage of this method is that it takes into account the Pauli principle, as well as the internal structure of interacting clusters. To study this problem, two semi-realistic nucleon-nucleon potentials were chosen: the modified Hasegawa-Nagata potential and the second version of the Volkov potential. Each of the potentials has its own unique characteristics and exchange parameters, which allows us to consider the presented problem in more detail. Based on the results of the work performed, the data obtained using two nucleon-nucleon potentials on the width Г and energy E of the resonance state were compared with the already available experimental data. As a result, there was a good agreement between theory and experiment.