A novel numerical model to estimate the mechanical behaviour of the new HL-LHC beam screen during a magnet quench is presented. The temperature rise due to the resistive losses of the induced currents is considered. This enables to refine the estimation of the Lorentz forces as they depend on the electrical resistivity of the materials, which in turn depends on the temperature. Compared to the analytical formulations used to design the current beam screen, the proposed model introduces four new features. Mechanical contacts have been set-up between multiple components, and the mechanical response of the beam screen is evaluated dynamically over the whole evolution of the quench. The pathways of the eddy currents are displayed on 3D geometries to better investigate the behaviour of any component placed along the beam axis. As the resistivity of some materials used for the beam screen is very low, self-inductance effects are included as well. These features make the estimation of beam screen behaviour more accurate.