Foundations are commonly situated on layered soil deposits, where the elastic stiffnesses may differ from values calculated using solutions for single-layer elastic media. This paper reports elastic stiffness coefficients for a rigid circular footing subjected to vertical, horizontal and moment loads bearing on a clay layer above a stiffer sand layer. Three-dimensional finite-element analyses considered various shear modulus ratios of top to bottom soil layers, as well as the thickness of the top layer below the footing. The elastic stiffnesses are presented as dimensionless coefficients and are bounded by published solutions for circular footings on a single-layer elastic half-space. Analytical expressions that capture the numerical results well are also proposed. The results can be used in the assessment of the elastic response of circular foundations on clay overlying sand, with applications in soil-structure interaction analyses of offshore structures among others.