Zusammenfassung By proper material selection, design and analysis, together with the applicable material testing-methods, bursting of pressure-vessels and pipings may be excluded, even if the components contain material defects to a certain degree. The methods of strength calculation applied are based on the ability of the material to plastic deformation, which therefore must be guaranteed under all service conditions and possible states of the material. This paper deals with unanswered questions in the field of safety-analysis. Some of these concern embrittlement phenomena caused by unfavourable states of stress — i.e. with multi-axial residual tensile stresses, so far not considered in fracture mechanics —, furthermore the effective material properties in the finished structural component (basic material, welded joints with local embrittlement and/or stress-relief embrittlement) including the influence of service conditions and the question of the allowable maximum nominal stress. In the case of seamless and normalized or quenched and tempered uncomplicated structure members, there exist relatively simple relationships between specimens or models and the real component. This is generally not true for thick-walled and/or welded structures even if the latter are stress relief heat-treated. Such structures may collapse at nominal stresses far below the yield stress, as soon as a critical value of the residual stresses is exceeded if simultaneously unfavourable material conditions exist. These statements are based on tests with unnotched and notched plates, pipes and pressure vessels with liquid and gaseous pressure media under static or repeated loading, furthermore on the analysis of damaged components.