The reliability analysis of structures, based on numerical models, involves computational efforts that are orders of magnitude higher than that of a single deterministic analysis of the model. This observation holds irrespectively of the analysis method used to quantify the reliability. Consequently, the applicability of reliability analysis to large-scale problems is frequently infeasible if the analysis is performed in a traditional, sequential fashion. High-performance computing, in particular the parallel execution of parts of the overall analysis task, can be used to turn the reliability analysis of industrial applications into a feasible task.The present contribution addresses the parallelization of advanced simulation methods for structural reliability analysis, which have recently been developed for large-scale structures with a high number of uncertain parameters. It is shown that for the Line Sampling method and the Subset Simulation method an essentially linear speedup can be achieved, for a moderate number of processors. In the presence of large numbers of processors, additional speedup is gained for Subset Simulation by using speculative computing -in the present application an additional speedup factor of three is shown to be feasible.