Numerical approximation methods for solving partial differential equations have been widely used in various engineering fields. In seeking an alternate numerical method using fewer grid points to find results with acceptable accuracy, the method of differential quadrature (DQ ) was introduced. This method is based on the ideas that the derivative of a function with respect to a co-ordinate direction can be expressed as a weighted linear sum of all the function can be approximated by a higher-order polynomial in the overall domain. This thesis deals with developing the DQ method for static and staibility analysis of cylindrical shells. First of all, having used the Flugge theory, the governed equations on the behavior of the shell under in-plane loads were formulated as a set of equations with displacement variables. Then, the goverened equations have been discretized on grid points and statically have been condenced to apply boundary conditions. A set of appropriate coputer programs have been developed to solve above-mentioned equations. Application of this method to various problems including shell problems showed that it has potential as an attractive numerical approximation technique. Furthermore, obtained results have been verified using some references.