The recently updated Italian standard adds, to the conventional safety assessment, the evaluation of the bearable maximum seismic action for existing concrete dams. This prescription actually represents a trend of current International guidelines that are gradually replacing the previous, deterministic safe/fail rationale and are accounting for nonlinear behavior. Depending on dam typology, a preliminary evaluation of the maximum bearable seismic action can be interpreted as the research of a capacity function for a given failure mechanism. In this work, the bearable maximum seismic action is investigated through numerical, three-dimensional, finite element simulations via a multipurpose code for two existing concrete dams placed in a region of low-to-moderate seismicity. In the first case, an arch-gravity dam, the overcoming of the limit stress conditions in wide parts of the bulk, the stiffness degradation in the global nonlinear response, and the displacement discontinuity in structural joints are used for the evaluation. In the second case, for a buttress-gravity dam, the sliding in the construction and foundation is instead considered.