In this study, strength deterioration and accumulation of deformation on two-story truss structures subjected to constant forces and repeated loading are investigated. Strength deterioration closely correlates with the accumulation of deformation, therefore the accumulation of deformation is considered to be a key parameter for the safety of structures subjected to repeated loading. The critical constant forces for convergence of the accumulation of deformation are calculated based on the proposed theory. The stability and bifurcation of the accumulation are discussed by using the critical constant force-displacement curves for convergence.