This research dealt with the linear elastic behavior of hollow core slabs resting on a linear Winkler type foundation. A finite difference method was used to model the slabs as wide beams and the foundation as elastic springs. The finite element method was also used to model the problem using ABAQUS 6.10 software program. A comparison between the method proposed in this paper and methods from previous studies was made to check the accuracy of the solutions. Several important parameters were incorporated in the analysis, viz. the hollow core size and shape, subgrade reaction and slab depth, to trace their effects on deflections, bending moments and shear forces. A computer program coded in Fortran was developed for the analysis of hollow core slabs on an elastic foundation. It was found that the maximum difference in deflection between the present study and the exact solution was 3% for the finite difference and 7% for the finite element method.