Abstract: This paper analyses elastic shell-bending problems by means of the least-square collocation method.The mixed method of MWR has been used in which the trial function-a double power series with unknown coefficients can meet the requirements of neither the differential equation of deflection in the interior of shell nor the boundary conditions. The computational results of cylindrical shells with 4 hinged edges show the errors less than 1.5 percent as compared with results of classical solutions,When analysing cantilever plate problems-a special case of cantilever cylindrical shell, the errors are also small. The calculation of all shell-bending problems can be generaly programmed by means of the method presented in this paper.