During operation, modern structures and their parts are subjected to complex cyclic loads. In this case, a complex stress-strain state can arise in products, which can lead to a significant decrease in their fatigue life. In this regard, the development of methods for predicting fatigue fracture of critical structures becomes urgent. The purpose of this work is to test a simple approach for describing multiaxial fatigue datasets presented in the literature and compare it with known multiaxial fatigue models. Within the framework of the study, actual experimental data was considered, containing experimental data on the multiaxial fatigue of aluminum alloys 2024-T3 and 2024-T4. The alloys are actively used in the designs of aircraft, ships and spacecraft. As a result, the Sines model and its modernized version were considered (taking into account the first invariant of the stress tensor with respect to amplitude values). At the same time, an approach was developed to determine the constants of the models based on the results of two variants of training experiments. The paper presents the results in the form of relationships of the predicted and experimental fatigue life, obtained using the Sines model and its modification for two types of training tests. In the final part of the work, a comparative analysis of the Sines model and its modification, Smith-Watson-Topper, Fatemi-Socie and its modification is carried out. The analysis showed that the modified Sines model significantly improves the predictive ability, the proposed model better described the experimental data than the traditional Sines model and the Smith-Watson-Topper approach. At the same time, the descriptive ability of the model is comparable to the Fatemi-Socie one.