Structural Sensitivity Analysis is performed using the direct differentiation method for buckling and free vibration problems of prismatic thin-walled structures employing the Finite Strip Method. The sensitivity of eigenvalues (critical stresses and free frequencies) with respect to variation of thickness of plate members and with respect to shape-type variations is considered. The differentiation is carried out employing analytical and semi-analytical methods. Numerical examples illustrate the sensitivity of thin-walled plates stiffened with ribs and thin-walled beams. The examples also serve for discussion of numerical efficiency and accuracy of the presented methods.