Because of limitations in exact solutions of engineering problems, researchers have tried to find approximate and numerical solutions. Finite element method is one of the most powerful and widely used approximation method of solving differential equations that has been used in the present study. One of the most important steps in the finite element method, is the choice of basis functions for the formulation of the element. In recent years the use of wavelets in numerical solutions of differential equations have been considered by many researchers. One of the applications of wavelets in numerical solution of differential equations, is to use it as a basis function in finite element method. Due to the high accuracy interpolation, daubechies wavelets are one of the most widely used wavelets in numerical analysis. In the present study daubechies wavelet of order 6 is used to formulate thin plate element. It is proved that this wavelet can exactly interpolate polynomials of order 5. Since these wavelets do not have explicit form, derivatives and integrals of these functions have been offered. In this thesis, by using of wavelet interpolate, the stiffness, force and geometry matrices will be derived for plates resting on elastic and point supports. Since many nodes are considered in the body and boundary of plate element, the point supports may be modeled without increasing number of elements. It will be shown that the results obtained wavelet method have very good agreement with the results reported else where. Because of high accuracy of wavelet interpolation, the number of element will be reduced. It will be shown that the increasing of elastic stiffness foundation for simply supported plate is more conciderable than clamped plates. Keywords: Plate bending, plate buckling, inelastic buckling, wavelet-based finite element method, daubechies wavelet, elastic foundation
