Abstract Identifying cracks and damages in structures using measured vibrational characteristics has received considerable attention in the past few decades. The possibility of using frequency changes due to the application of a mass appended to the structure has also been considered. In this paper an analytical proof to show that the natural frequencies of a cracked beam with a roving body possessing mass and rotary inertia will generally change abruptly as the body passes over a crack, provided that the crack permits differential flexural rotations, is presented. A novel explicit closed form solution of the governing equation of an Euler-Bernoulli beam with a roving body possessing mass and rotary inertia, in the presence of multiple cracks is also proposed. The presented exact solution is used to conduct a parametric analysis of cracked beams. Numerical results for natural frequencies are provided and a procedure to exploit the occurrence of frequency shifts to detect and locate each crack, without having to perform any additional calculation, is described.