Determination of nonunique configurations of structures is a problem which cannot be treated readily using classical methods of analysis. In the literature, these kinds of problems are tackled for some simple problems, like trusses with a small number of joints and members, and with specially designed approaches. The recent method of analysis called Total Potential Optimization using Metaheuristic Algorithms (TPO/MA), on the other hand, provides an efficient tool for dealing with these kinds of problems, practically without recourse to any special arrangement. In this analysis, using Harmony Search as the metaheuristic algorithm, large truss structures with linear elastic members are investigated under large deflections as to the existence of more than one solution. The results have shown that for the two examples investigated, a tower truss with 25 members and a dome truss with 24 members, nonunique configurations do exist at quite unexpected levels of loads, and that only one of them can be found with normal applications of the well-known Finite Element method.