The spatial distribution of dynamic strain is determined by the modal shape and hence the strain at a certain area can be reduced by modal shape design. Based on the proportional relation between strain and curvature, this paper proposes an integral method to solve curvature modal frequencies and shapes directly of cantilever beam-like structures with variable stiffness and mass functions. The method is validated by comparing the computation results with both numerical and analytical solutions. Furthermore, the presented method transforms the problem solving of continuous systems modes into a generalized eigenvalue form of finite degrees of freedom. The explicit expressions of curvature eigen-sensitivity have been established with Nelson's method, and the curvature gradient modes are also calculated to show the change of dynamic strain more visibly. An example of parameter design is presented with the proposed sensitivity analysis method. Moreover, this method is proved capable of treating the other two boundary conditions of clamped-simply supported and clamped-clamped.