This paper adresses the issues that arise when setting strength conditions due to its complexity in the form of testing devices and the excessive number of combinations of the actions that each material can be subjected to. That problem has very well approximated by reducing the triaxial stress condition to uniaxial with various strength theories. Each of the theories is discussed and explained separately. Therefore, it is possible to distinguish all of their advantages and disadvantages and to examine the compatibility of a particular theory with the experimental results from practice. Furthermore, cross comparisons between strength theories and the connection between strength theory and material ductility are also shown. Thus, some theories are going to indicate excellent compatibility with experimental results for the elastoplastic materials, while the same theories will give insufficient results for the brittle materials and vice versa. Finally, the application of strength theories in practice (sizing the diameter of the rod, determining the factor of safety for the material and determining the most dangerous of the various stress states according to all strength theories) is shown in numerical examples.