Abstract The reliability of nuclear structures relates directly to the reliability of mechanical and electronic systems. Nuclear structures may be viewed as part of operational system as well as part of standby safety system. Except for proof loading, most of the load types, seen by nuclear structures, such as containments, primary piping, etc. during their design life, are random in time and space. Structural resistances, governed mainly by the respective material properties show also random characteristics. Methods of structural reliability, as discussed here, provide the means to process rationally the available information. Hence, they are an indispensable tool within the frame work of probabilistic risk analyses (PRA's). The probabilistic analysis is exemplified by determining the reliability of a containment structure sited in an area with strong seismicity.