Abstract: The dynamic responses of a type of beam are investigated, the cross-section and inertia moment of which vary with power functions. Natural frequencies and vibration modes of the beam are calculated by semi-analytical method. Comparison of the solutions with finite element solutions is conducted to verify the accuracy. Considering convected inertial force, relative inertial force, Coriolis force and centrifugal inertial force, equations for transverse bending vibration of the beam under moving mass are derived and solved numerically using Newmark method. The dynamic response of a cantilever beam with variable cross-section and inertia moment is analyzed in a case study, which verifies the proposed approach.