The electromagnetic modeling of practical finite periodic structures is a topic of growing interest. Due to the truncation of infinite periodic structures, surface waves will be excited and localized near discontinuous interfaces leading to the edge effect. In this work, surface waves are numerically extracted and their magnitudes and decay rates are analyzed for different materials and geometries. Based on the exponential decay of the surface wave, a novel method is developed by connecting the solution to the large finite array problem with that to a relatively small one to achieve low complexity and memory consumption. The method numerically reconstructs propagating Bloch waves and surface waves according to the Bloch-Floquet theorem of periodic structures and translation invariant properties of semi-infinite periodic structures, respectively. Numerical examples are shown for near-field distributions and far-field radiation patterns. The results obtained from small finite periodic structures capture the edge effect and agree well with the results by the rigorous element-by-element approach.