Yield stresses, allowable stresses, moment capacities (plastic moments), external loadings, manufacturing errors are not given fixed quantities in practice, but have to be modelled as random variables with a certain joint probability distribution. Hence, problems from limit (collapse) load analysis or plastic analysis and from plastic and elastic design of structures are treated in the framework of stochastic optimization. Using especially reliability-oriented optimization methods, the behavioral constraints are quantified by means of the corresponding probability ps of survival. Lower bounds for ps are obtained by selecting certain redundants in the vector of internal forces; moreover, upper bounds for ps are constructed by considering a pair of dual linear pro-prams for the optimizational representation of the yield or safety conditions. Whereas ps can be computed e.g. by sampling methods or by asymptotic expansion techniques based on Laplace integral representations of certain multiple integrals, efficient techniques for the computation of the sensitivities (of various orders) of ps with respect to input or design variables have yet to be developed. Hence several new techniques are suggested for the numerical computation of derivatives of ps.