Abstract: The solution of differential equations’MWR is approached in this
paper, It is proved that the minimum of the square functional I(u) of this method is existent, Then，the shear deformation theory of cylindrical
shells is established. By using the method in examples，the precision of
the shear deformation theory of cylindrical shells is analysed(its funda-
mental relations contain five second-order partial differential equations of
two variables).The results show that the solution of differential equat-
ionsl MWR is successful，and the precision of the shear deformation
theory of cylindrical shells is satisfactory.