A spectral element method for analyzing wave propagation in multiply connected plates oriented at arbitrary angles is presented. These plate elements may be joined to model structures with stiffeners, open or closed thin-walled tubes, corrugated plates, channels, and ducts. The element models exactly both in-plane and out-of-plane responses over large domains. Results for point impact of a plate with stringers and a thin-walled box beam show excellent agreement with finite element solutions.