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The reliability with respect to plastic collapse of rigid frame and truss structures is estimated by directional simulation. This conditional expectation simulation method is especiahy attractive for this problem because the mechanical computation for each sample is the same as the computation required in a standard Monte Carlo simulation. For each simulation a mathematical programming problem must be solved. Under suitable conditions this programming problem simplifies to a linear one. How results from methods of identifying likely plastic mechanisms can be used to establish an importance sampling whereby the sample size can be reduced without loss of accuracy is shown. Finally, it is shown how parametric sensitivity can be estimated by directional simulation.