A parallel-plate pair with complex shared antipad structures was analyzed by decomposing it into rectangular local via structures and the plate pair region by virtual interfaces. The rectangle local via structures and the connections between via structures and the plate pair region were rigorously studied. An innovative cavity-based partial-element equivalent-circuit (PEEC) formulation was used to model the rectangle via structures. With special treatment of the reference in the PEEC equivalent circuits, improved circuits model was achieved and all elements of the circuits had clear physical meanings. Furthermore, by enforcing the continuity of the tangential electric fields at the virtual interfaces, the rectangle local via structures were able to connect to the plate region. The impedance parameters of several kinds of rectangle via structures and the whole parallel-plate pair were obtained using the proposed method, and the accuracy of the results was validated with the finite-element solution from a commercial tool.