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Complex via structures such as noncircular antipads are rigorously studied, in the local region close to vias, using an innovative partial-element equivalent-circuit (PEEC) formulation based on the cavity Green's functions. The problem under study is an essential building block that can be used to model complex multilayer structures. With the usage of the cavity Green's functions, the number of unknowns is significantly reduced. Further, nonorthogonal quadrilateral mesh is used to better accommodate the complex shape of the antipads in practical designs. A novel wave port excitation method is proposed, which is new for the PEEC formulations. Singularity extraction in self element calculations involving the nonorthogonal cell and the cavity Green's functions is studied. The impedance parameters of several via structures are obtained using the proposed method, and the results are validated with the finite-element solution from a commercial tool.