This study is aimed to examine the minimum required thickness of U-shaped ribs for the laminated composite plates under in-plane uniaxial compression. 3-dimensional finite element models for the U-rib stiffened plates were setup by using ABAQUS and then a series of eigenvalue analyses were conducted. The minimum required thickness was compared by applying the orthotropic plates with the eight layer composite layups of [(0°)4]s, [(0°/90°)2]s and [(-45°/45°)2]s. There is a need to develope a simple design method to determine the minimum required thickness of U-shaped ribs, which should require more much parametric analysis results than a series of data shown in this study. This study will contribute to the future study for establishing the optimum design method of U-rib stiffened plates.