Shielding effectiveness (SE) estimation for an enclosure with apertures has been an attractive issue in electromagnetic compatibility (EMC) research area. Though many fast algorithms are developed for SE calculation, they mainly focus on the case of single cavity. Moreover, most of these methods neglect the wave coupling through apertures from enclosure to outside. A fast algorithm based on electromagnetic topology is proposed for calculating the SE of cascading multiple enclosures with apertures. In this algorithm, the wave coupling through apertures in both directions is taken into consideration. Firstly, the equivalent circuital model of cascading double enclosures and its signal flow graph of electromagnetic topology are given, followed by the derivation of scattering matrix of apertures node. Then propagation relationships at tube level and reflection relationships at node level are derived. As a result, the general BLT (Baum-Liu-Tesche) equation for voltage calculation at each node is established. Two major categories of cascading three enclosures with apertures are investigated. For serially cascading three enclosures, the general BLT equations are extended on the basis of BLT equations for cascading double enclosures, since the structures are a simple extension of them. For hybrid serially-parallelly cascading three enclosures, the common walls between the main enclosure and two sub-enclosures are considered as a topological node represented by a three-port network, whose scattering matrix is derived according to the definition of scattering parameters. Consequently, the general BLT equations for hybrid serially-parallelly cascading three enclosures are developed. Compared to the algorithms presented in the relevant literature, the topology-based algorithm proposed in this paper can not only calculate the shielding effectiveness for cascading multiple enclosures, but also lead to more accurate results in that the impedance of apertures is obtained through using diaphragms model. In order to validate the proposed method, a cascading double enclosures from a literature is chosen as an example. Calculated SE results are in good agreement with those in the literature. Then, three enclosures with different configurations and dimensions are also designed to validate the proposed method. Results from the proposed method are compared with those from the finite difference time domain (FDTD) method, and they are found to be in good agreement with each other. Experimental results also demonstrate the validation of the proposed method. Especially, the proposed method takes far less time to calculate SE than for FDTD method.