In this study, the dynamic characteristics of cantilever shear beams with a uniform mass and parabolic reduction of lateral stiffness along its length are examined. Closed-form expressions to mode shapes and frequencies of vibration are developed in terms of first and second order Legendre functions. It is shown that proposed expressions provide dynamic characteristics that agree with those computed with detailed finite element models, therefore, showing that they are the true solutions to the problem at hand. The effect of reductions in