Abstract: In this paper, the objective is to enrich the existing 1D and 2D mass-spring models with physical accuracy as well as visual realism. It is found that using nonzero preloads on the springs is a necessary condition for the models to approximate their continuum counterparts. First, the parameters of the 1D mass-spring model of a beam are derived based on pure bending and axial action. It is proved that the mass-spring model with this set of parameter has correct characteristics of resistance against lateral displacement, which is one of the most important aspects of the accuracy of the 1D mass-spring model. Then, the method is extended to the 2D mass-spring models of the continuum plate with two different mesh structures. The mass-spring model with equilateral triangle meshes is shown to be physically more accurate than that with rectangular meshes. Finally, the physical accuracy that the mass-spring models with preload can achieve is investigated under different load conditions by comparison with the finite element method (FEM) to demonstrate the efficacy of our approach.