Plates are structural components used as walls, roofs, panels, windows, etc. They are modelled as two-dimensional structures characterized by a plane geometry bounded by a contour comprising straight and/or curved lines. Plates are intended to resist various load conditions, broadly classified as in-plane and out-of-plane loads, that is forces either parallel or perpendicular to the plane of the plate, respectively. It is found convenient to study their response properties by separating first the in-plane and the out-of-plane motions. In-plane motions of plates are generally marked by the coupling between the two in-plane components of the displacement field. Such a coupling gives rise to new interesting features of in-plane motions with respect to the longitudinal motions of straight beams. Coupling between in-plane and out-of-plane motions occurs in the presence of in-plane preloads and will be considered in the next chapter. On the other hand, for mathematical convenience in using Cartesian coordinates, presentation will focus first on rectangular plates. Then use of curvilinear coordinates will be introduced to consider plates bounded by curved contours.