The variational technique is applied to calculate the stresses for a thin-walled structure composed of a closed cell connected to a four-flanges open cell. The structure has one built-in end, the other end is free, loaded by torque moment,a rectangular model is constructed for application of the obtained general results found by variational technique. Experimental measurements are carried out on it using semi-conductor strain gauges. The theoretical and experimental results of normal stress distribution in flanges are in good agreement.