This study is devoted to tracing the equilibrium path of structures with severe nonlinear behavior. A new displacement increment is suggested to do the analysis. Moreover, the increment of the load factor is obtained by minimizing the residual displacement. To evaluate the capabilities of the presented method against existing ones, a comparison study is performed. In this process, five benchmark frame and truss problems are solved. Each of the structures is analyzed more than 600 times, and the outcomes are compared with each other. According to the results, the authors' scheme is more competent than the methods of residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control and modified normal flow.