In this study, a method is presented for free vibration analysis of multi-storey asymmetric structures whose bearing system is composed of shear walls and cores. The multi-storey structure was modeled as an equivalent cantilever beam in the study. The equivalent cantilever beam in the method was divided into as many finite elements as the number of the storeys. In the study first of all, a differential equation belonging to the equivalent cantilever beam was written for ith storey by using the calculation model in the continuous system. Then, a stiffness matrix for ith storey was obtained using the solution of the written differential equation. The masses in the model were applied on the storey levels. Angular frequencies were obtained using the system mass matrix and system stiffness matrix formed by storey stiffness matrices. At the end of the study, a sample taken from literature was solved and the results were evaluated to test the convenience of the method.