As an alternative structural analysis method, total potential optimization using metaheuristic algorithms (TPO/MAs) has been demonstrated to be very effective, especially in nonlinear cases, for trusses and trusslike systems such as tensegric structures and cable networks. A recent study showed that TPO/MAs also can be applied successfully to plane-stress problems with linear constitutive equations. The present study enlarged the application area of TPO/MAs to the analysis of plates for plane-stress cases with nonlinear stress-strain equations. A relevant formulation was developed and used to solve five problems. Because TPO/MAs can be applied by using different metaheuristic algorithms, a number of them, some hybrid, were used, and they were compared among themselves and with finite-element solutions. The final example was a tunnel problem with 150 nodes, i.e., with 265 unknowns. This problem also was solved via hybrid algorithms. Several proposals for future research are listed. (c) 2020 American Society of Civil Engineers.