When a plate structure is externally loaded, structural elements such as stiffened plates and panels are usually subjected to combined stresses. As practical examples of such combined stresses in ship structures, compression and shear, compression and lateral pressure and so on may be cited. In our previous paper, the ultimate strength of a square plate subjected to compression and shear was analyzed as one of basic studies on the strength of the plates under combined stresses. In this paper, the ultimate strength of rectangular plates subjected to compression and lateral pressure is investigated in order to know the strength of bottom plates of ship structures. The analytical method from the previous paper is extended and applied to this problem. The analyses are carried out for the plates of various aspect ratios (β=1, 2 and 3). The obtained results are in good agreement with experimental ones conducted by Yoshiki·Yamamoto et al. The following conclusions are obtained, 1) Lateral pressure reduces compressive strength of plates. Especially in case of square plates, the reduction of the compressive strength is almost uniform in spite of the variation of breadth-thickness ratio of plate. 2) As for a rectangular plate with the aspect ratio β=2 or 3, in case of small lateral pressure the collapse mode of the plate shows buckling pattern. On the other hand, in case of large pressure, the collapse mode becomes another pattern which is characterized by lateral pressure. From the above, the limit pressure p^*_c can be defined as the intersection of two curves which show the strength of the respective modes. 3) When a plate collapses in the mode of buckling pattern, the reduction of compressive strength due to lateral pressure is rather small. However in case of the collapse with the other pattern which is induced by lateral pressure, the reduction of that is considerably large because of the effect of the bending stress generated by the lateral pressure.