This paper presents the analytical investigations pertaining to the elastic buckling behavior of orthotropic composite plates. By the pultrusion process the structural shapes composed of orthotropic plate components are readily available in the construction market. When the member is utilized for the flexure, lateral-torsional buckling and local buckling behaviors must be taken into consideration. In the local buckling analysis, flange and web local buckling analyses must be conducted in the design of such a member. For finding the web buckling strength, the buckling equation for the orthotropic plate under linearly distributed in-plane forces is derived by using the Rayleigh-Ritz method. The boundary conditions of plate are assumed that the loaded edges are simply supported and the unloaded edges are simply supported or fixedly supported. The buckling coefficient of a plate having different orthogonal mechanical properties is found by using the numerical technique and the minimum buckling coefficient is suggested. In addition, simplified form of equation for predicting the minimum buckling coefficient for the plate is proposed. Brief discussion on the design criteria relating to the web local buckling is also provided.