A connection algorithm is presented for analyzing the electromagnetic scattering from arbitrarily shaped open cavities. This approach allows different sections of the cavity to be analyzed independently of one another. The aperture admittance matrix representation of each region is generated using the boundary-integral method. Applying the concept of input and load admittance, a connection algorithm is developed to cascade all the aperture admittance matrices together to form the aperture admittance matrix of the entire cavity. Finally, the aperture electric field can be found from the generalized network formulation and the backscattered field can be determined. Numerical examples are presented to demonstrate the advantages of this algorithm that include modeling flexibility and reduced computational resources.