An analysis is presented for nonbifurcational behavior of flat and curved panels of unsymmetrically laminated composite materials under in-plane loading, either compression or shear. A pair of governing equations in the von Karman sense are solved in conjunction with simply supported boundaries. A series of computations is carried out for panels having different curvatures, different lay-ups, and different materials. The results show that during loading, lateral deflection is involved in panels with unsymmetric cross-ply layers under compression or in those with unsymmetric angle-ply layers under shear. This effect increases deflection of the flat plates under loading and reduces resistance of curved panels against collapse.