The advantage of using reinforcing substrate layers with phosphor screens is that they increase the phosphor sensitivity and filter the scattered radiation, while providing a mechanical support for the phosphor layer. A simulation model based on the Monte Carlo code Geant4 was developed to study the influence of the substrate properties (material, thickness) on the phosphor screen spatial response. The optimal substrate/phosphor combinations have been determined at given sensitivity of the screen. Of all studied cases at medium energy (300 keV), a configuration with slight improvement in the screen spatial response has been found. Moreover, the results show that, without degrading the performances of the screen, the phosphor thickness may be significantly reduced (by 35% in the case of a 0.05 mm Pb substrate). Besides, PolyEthylene Terephthalate (PET) makes a good mechanical support (of up to minimum 4 mm in thickness) for the phosphor layer. The simulation methodology permitted to study the role played by the X-ray and electron processes inside the substrate layer.