In general, cylindrically curved plates are used in ships and offshore structures such as wind towers, spa structures, fore and aft side shell plating, and bilge circle parts in merchant vessels. In a number of studies, it has been shown that curvature increases the buckling strength of a plate under compressive loading, and the ultimate load-carrying capacity is also expected to increase. In the present paper, a series of elastic and elastoplastic large deflection analyses were performed using the commercial finite element analysis program (MSC.NASTRAN/PATRAN) in order to clarify and examine the fundamental buckling and collapse behaviors of curved plates subjected to combined axial compression and lateral pressure. On the basis of the numerical results, the effects of curvature, the magnitude of the initial deflection, the slenderness ratio, and the aspect ratio on the characteristics of the buckling and collapse behavior of the curved plates are discussed. On the basis of the calculated results, the design formula was developed to predict the buckling and ultimate strengths of curved plates subjected to combined loads in an analytical manner. The buckling strength behaviors were simulated by performing elastic large deflection analyses. The newly developed formulations were applied in order to perform verification analyses for the curved plates by comparing the numerical results, and then, the usefulness of the proposed method was demonstrated.