This report addresses a crack-growth driven by mixed modes and fracture failure assessment of mechanical components in nuclear power facilities. Analytic solutions to stress fields and the energy release rate of the crack are reviewed and examined for cases when the crack propagates straight-ahead (Mode I cracking) and in a kinked direction (Mixed mode cracking). It is illustrated that for cases when complex loading conditions or dissimilar materials are under consideration, the energy release rate for a straight-ahead growth can be much less than that for a kinked growth. Hence, for such cases the crack growth is inevitably driven by mixed modes and the mode mixity must be taken into account in the fracture assessment. Otherwise, the fracture failure cannot be evaluated correctly. Numerical studies are conducted and it is shown that it is not conservative to use a purely mode-I based criterion for the evaluation of the fracture failure assessment for typical problems of mixed mode driven cracking. Suggestions for accounting the effect of mixed mode cracking in connection to the application of the R6-approch for safety assessment are given.