General expressions of crack perturbations are given with perturbation method. With the delta function to express the crack position at the simple beam, the expressions of cross-section rotary inertia and mass per unit length of the whole beam are founded, and then the transverse free vibration equation of the simple beam with a damaged crack is established. The first and second order perturbations are considered as the linear combinations of corresponding mode shapes of intact state, according to the boundary conditions, and theoretical solutions about eigenvalues and mode shapes of the damage state are finally obtained. One simple beam is taken as a numerical example to calculate the modal parameters; the effects of first and second order perturbations on the results are compared. It is believed that the approach proposed in this paper could provide the necessary theoretical background for damage identification in simple beam.