In this thesis, the calculation of uniaxial and multiaxial stress-states using strength theories is specified. The problem of determining critical values of principal stress can arise when analysing multiaxial stress-states because of a large number of combinations and the complexity of the testing apparatus. Because of the reasons referred to earlier, strength theories have been introduced. They are used for reducing multiaxial stress-state to uniaxial stress-state, which are equivalent when considering the occurrence of a fracture or plastic deformation. Several theories are explained, along with advantages and disadvantages. Furthermore, certain overlaps of experimental data for elastoplastic or fragile materials and strength theories results have been determined. After each strength theory was explained, a comparison between different strength theories was made and the connection between each one and the ductility of the used material was defined, which means that the same theory will give different results, depending on the type of material. At the end of the thesis, using a numerical example, an application of a specific strength theory in practice was shown by dimensioning several cross-sections.