The paper presents results of evaluation of common tests for fracture characterization of advanced high-strength sheet steels with the help of the FEA. The tests include three in-plane shear tests, two uniaxial tension tests, two plane strain tension tests and two equibiaxial tension tests. Three high-strength steels with different yield loci, strain hardening rates and strengths in three different thicknesses each were used. The evaluation was performed based on the spatial distribution of the equivalent plastic strain and damage variable in the specimen at the moment of crack initiation as well as on the time variation of the stress state at the crack initiation location. For in-plane shear, uniaxial tension and plane strain tension, no test can be unconditionally recommended as disadvantages of all studied tests in these groups cannot be neglected. However, in each of these groups, a test can be chosen, which represents an acceptable compromise between its advantages and disadvantages: the shear test on an IFUM butterfly specimen for in-plane shear, the tensile test on a holed specimen for uniaxial tension and the tensile test on a waisted specimen for plane strain tension. On the contrary, the bulge test on a circular specimen with a punch of Ø 100 mm can be unconditionally recommended for equibiaxial tension. In the future, optimisation of the studied tests for in-plane shear, uniaxial tension and plane strain tension appears to be necessary.