The composite element method is utilized to discretise a stepped Euler-Bernoulli beam with a crack. The local stiffness reduction due to the crack is introduced by using a simplified crack model. The finite element equation for the forced vibration analysis is obtained using the composite element method (CEM). The forced vibration response of the cracked stepped beam is numerically calculated using Newmark integration method. Numerical results indicate that the position and depth of a crack affects the low and high natural frequencies and modes of a cantilever beam, respectively. And the position of the crack has significant effects on the dynamic responses of the beam.