Earthquakes pose a serious threat to historical masonry structures. Their high mass, negligible bonding strength and weak connectivity among members often trigger out-of-plane mechanisms, which are susceptible to collapse. When a wall has constrained boundary conditions on its top and base, it undergoes out-of-plane bending along its height, forming the Vertical Spanning Strip Wall (VSSW) mechanism. This mechanism consists of three hinges and two macro-blocks that experience highly nonlinear dynamic behaviour. Moreover, the VSSW response is strongly affected by the presence of an overlying wall or diaphragm, as well as a diversity of diaphragm-to-wall connections. This study develops and presents an efficient numerical model that simulates the influence of these aspects on the dynamic response of the VSSW. Specifically, the proposed model resorts to analytical rocking dynamics and analyses the VSSW as a two-rigid-body single-degree-of-freedom system, explicitly accounting for overburden mass and a variety of boundary conditions. The equation of motion of the system is derived using Lagrangian dynamics, together with closed-form expressions that quantify the energy losses during impacts. Consequently, the model is subjected to a series of free and forced rocking analyses to highlight the significance of the boundary conditions and overburden mass on the dynamic behaviour of the VSSW.