The three-dimensional theoretical solution of a concentrated normal force acting on the free surface of a coated material has been deduced by applying the reflection method. It is found that all stress functions defined in the local coordinate systems with their origins placed at each mirror point can be deduced from the fundamental solution of a concentrated normal force acting on the free surface of a semi-infinite homogeneous medium. The structure of the elastic solution has been illustrated by numerical analysis. It is found that only the stress functions corresponding to the first few mirror points are influential It is also found that the effect of material combination on the stresst field shall be described by three parameters, the two Dundurs' parameters and one additional parameter.