A geometrically-nonlinear displacement method is developed for the purpose of studying the snap-through behavior of reticulated space trusses of arbitrary shape and loading. The present formulation is comprehensive and well suited for applying incremental and iterative solution techniques solving the governing system of nonlinear equations. The results of comparative studies of four efficient solution methods are presented with reference to the computational efforts. The dramatic influence of nonuniform loading and unsymmetrical stiffnesses on the snap-through load is shown by parametric studies.