Abstract: In this paper,the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms.By assuming proper form of series for deflection,the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations.Because the boundary of contact region cannot be determined in advance,these equations are weak nonlinear ones.They can be solved by using iterative procedures.