Both problems of bending considering transverse shear deformation and plane stress of circular plates on elastic foundation are discussed in this paper. The elastic foundation is assumed to be Winkler type. General solutions of the differential equations which govern these problems are presented as analytical solutions of the circular plates on elastic foundation under axi-symmetric and non-symmetric loading conditions. The well-known theory of Reissner is applied to the problems of bending considering transverse shear deformation. These presented solutions are formulated closed forms. They consist of the modified Bessel functions of the first kind of order n and so forth. It is very important to adopt displacement functions in order to obtain the analytical solutions for both problems of bending considering transverse shear deformation and plane stress of the circular plates on elastic foundation under non-symmetric loading conditions.