In this paper, as a basic study on the compressive strength of a ship's bottom plating, the behaviour and the strength of simply supported long rectangular plates (aspect ratio α=3 and 4) having in-plane constraint in the transverse direction under increasing compression and constant hydrostatic pressure, are studied theoretically and experimentally following the previous paper. Results obtained in this study is summarized as follows : (1) The basic equation for pursuing the elastic behaviour of the plate in which long sides are transversely immovable ( e_y =0) under such combined loads, is shown by using the large deflection theory. Carrying out the analyses based on this equation, characteristics of behaviours including buckling phenomena are clarified. (2) The compressive strength of such a plate is calculated by assuming that the plate behaving elastically up to collapse fails when it will satisfy the condition of plastic collapse. In this case, the tendency of the variation of the compressive strength due to hydrostatic pressure is similar to that obtained for plates having no in-plane constraint ( p_y =0) in the previous paper. (3) Moreover, the effect of the in-plane constraint on the compressive strength is also discussed by comparing the above results with those for plates in the case of P_y =0. (4) Performing tests for two kinds of thin plates (α=3) having comparatively large value of ( b / t ) √σ _Y / E , the obtained results on behaviours including buckling phenomena and compressive strengths are in good agreement with theoretical results.