This paper examines a beam with open cracks, which is regarded as a non-uniform beam. Based on the Bernoulli-Euler beam theory, the semi-analytical solution of dynamic characteristics of a simply supported beam and continuous beam with an arbitrary number of open cracks was obtained using the modal perturbation method. In the modal subspace of the uniform beam, the variable coefficient differential vibration equation of the non-uniform beam was converted to nonlinear algebraic equations. The modal parameters of the cracked beam were solved using the natural frequency and vibration mode of the uniform beam. The dynamic test analysis of the simply supported beam and two-span continuous beam with rectangular open cracks indicated that the semi-analytical solution was highly precise. Finally, the sensitivity of the natural frequency to crack parameters was studied using the semi-analytical solution of dynamic characteristics of the beam with open cracks.