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Structural reliability analysis is based on the concept of a limit state function separating failure from safe states of a structure. Upper and lower bound theorems of limit and shakedown analysis are used for a direct definition of the limit state function for failure by plastic collapse or by inadaptation. Shakedown describes an asymptotic and therefore time invariant structural behavior under time variant loading. The limit state function and its gradient are obtained from a mathematical optimization problem. The method is implemented into a general purpose finite element model (FEM) code. Combined with first-order methods/second-order methods (FORM/SORM) robust and precise analyses can be performed for structures with high reliability. This approach is particularly effective because the sensitivities which are needed by FORM/SORM are derived from the solution of the deterministic problem.