The algorithm of fatigue life determination for machine elements subjected to random loading uses fatigue characteristics of the material determined under constant-amplitude loading. They are usually stress or strain characteristics as well as characteristics using the energy parameter. Their correct selection influences correctness of the obtained results related to the experimental data. The paper presents analysis of convergence of the calculated fatigue lives of some constructional materials subjected to random loading under uniaxial loading state. For calculations concerning one material the same loading state was assumed and fatigue characteristics were determined on the basis of one data set obtained under constant strain amplitude tests. Calculated fatigue lives based on different fatigue characteristics were compared and their convergences were tested. It has been proved that convergences are different depending on the material. The comparison results were presented in form of graphs.