Using a modified Vlasov model, the present study (PS) uses a functional system to analyze a transversely loaded slab with a two-parameter elastic foundation. To estimate the two soil parameters of the Vlasov foundation, the soil modulus and Poisson’s ratio are assumed to be constant from the upper surface to the top of the lower rigid foundation. The Finite Element Method (FEM) develops all deformation stiffness matrices of plates and soils. For the present formulation, MATLAB code was written. Once the results are contrasted with those of related studies conducted by other researchers, they demonstrate excellent consistency. The current method is exceptionally effective in convergent analysis of slabs with two-parameter Vlasov foundations and is simple, efficient, and dependable. It requires less computing work, time, and resources and is a straightforward approach to get results for stress.