This study widely investigates the ultimate bearing capacity of a rigid footing on the free surface of sand overlying clay using the rigid plastic finite element method (RPFEM). Interface elements were introduced with the new constitutive equations developed by the authors to properly evaluate the interaction between the footing and the soil, as these elements greatly affect the failure mechanism of the footing-soil system. Two friction conditions were employed for the footing surface, namely, the perfectly rough condition and the perfectly smooth condition. The RPFEM was extended to calculate the distribution of contact normal stress along the footing base corresponding to changes in the thickness of the sand layer. Several design charts were developed to directly determine the ultimate bearing capacity by increasing the internal friction angle, the thickness of the sand layer, and the shear strength of the clay layer. Two cases were considered for the clay layer below the sand layer, namely, a weak layer and a stiff layer. The failure mode of two-layered soils was found to change from the general shear mode to the punching shear mode for both friction conditions by a reduction in the shear strength of the clay layer. The sheared area of the ground was limited to the sand layer in the general shear mode, while the sheared area was distributed throughout the two layers in the punching shear mode. New bearing capacity formulas during the punching shear mode were proposed for the two friction conditions in a wide range of strength and geometric parameters, which were in close agreement with the experimental studies and are efficient enough to be used in practice.