Plastic deformation of plates in steel deck structures under heavy vehicle or helicopter wheel loads is common in ships and offshore structures, and is therefore of significant interest to designers of ro-ro/cargo ships, helicopter-carrying ships and offshore platforms. To provide insight into the plastic deformation of plates, the nonlinear elasto-plastic response of stiffened steel plates loaded quasi-statically by a central rigid rectangular indenter is investigated both experimentally and numerically. The numerically-determined stiffened plate permanent deflections compare well with those obtained experimentally. The concept of applying the elasto-plastic method to the design of deck plates under wheel patch loads is introduced, and the design principle of wheel patch loaded plating is studied together with the design criteria. A simple design formula to determine plating thickness is proposed based on an acceptable level of permanent set. Ship-mounted helideck plating design cases are given to illustrate the elasto-plastic method, and comparisons are made between the thicknesses derived using the proposed design formula and those found from Lloyd's Register (LR), Bureau Veritas (BV) and DNV-GL rule requirements.