The Basic Theory of the deflection of long, thin plates under normal pressure is extended to cover the effects of initial lateral tension or slackness in the plate and the effect of deformation of the supports at the edges of the plate under the lateral tension developed. The procedure is illustrated by application to a case of a plate under initial tension with its edges held apart elastically, and the computed values of the strains are compared with values measured experimentally. The application to an initially slack plate is also illustrated by a diagram.