【Objective】To carry out research on damage identification and state assessment of bridge structures, this paper makes a comparative study on two analytical methods for dynamic characteristics of cracked simply supported beams. [Method] Based on the basic ideas of transfer matrix method and segmented mode function method, a massless torsion spring was used to simulate the local flexibility caused by cracks. Two solving methods for the dynamic characteristics of simply supported beams with arbitrary numbers of cracks were derived using recursive method and Heaviside function, and compared and analyzed with the finite element results of ANSYS.【Result】For single-crack, double-crack, and triple-crack beams, both methods yielded results that are well matched with the finite element results, demonstrating high computational accuracy. Compared to the transfer matrix method, the segmented mode shape function method exhibits higher computational efficiency in calculating the natural frequencies of beams with multiple cracks, especially for higher-order frequencies. The maximum difference in computation time under triple cracking is 16.51 seconds. As the number of cracks increaseds, the computation time for natural frequencies using the transfer matrix method increases to 2.85 times and 13.30 times, while for the segmented mode shape function method is increasing to 1.10 times and 5.43 times. The computation time using the transfer matrix method significantly increases and shows an exponential growth trend. The variation in crack depth has a minor impact on computational efficiency.【Conclusion】Exploring the impact of crack depth and quantity on the computational efficiency of two methods has significant practical significance for improving the efficiency and accuracy of bridge structural damage identification.