Abstract: An analytical solution of a nonlinear single degree of freedom (SDOF) model was developed with a tri-linear resistance function capable of describing various forms of structural resistance, and a loading function consisting of a linear ascending part with an ensuing constant value. The model considered the effect of catenary action and the column removal time on the dynamic structural response. The SDOF model is expected to accurately predict the displacement response of substructures in progressive collapse, as validated by the comparison between the analytical results and experimental data. As a result, the model can be implemented for dynamic analysis of substructures subjected to progressive collapse.