The structural shapes or plates with varying thickness are often adopted in aerospace industries such as a skin structure of an airplane and civil engineering fields where the load effects are varied along the longitudinal axis of the member. Specially, the structural steel tapered plate, so called LP (longitudinally profiled) plate, has been used in many countries as a part of main member of bridges, buildings, etc. This paper presents the result of an analytical study pertaining to the local buckling behavior of FRP (Fiber Reinforced Plastic) flexural member. The flexural member is consisted with uniform thickness web and flange tapered in thickness. The boundary conditions of flange plate in its unloaded edges are elastically restrained, but they are assumed to be either fixed-free or simple-free for simplicity. In the analysis, the Galerkin form of Rayleigh-Ritz method is adopted. The buckling equation of isolated unstiffened tapered plate elements having fixed-free or simple-free boundary condition in its unloaded edges is derived. The plate buckling coefficients with respect to the thickness ratios and plate aspect ratios are calculated and presented in a graphical form. Unlike the buckling of plate with uniform thickness, discontinuous changes of buckling mode are not exist. In addition, the critical slenderness ratio of such an unstiffened tapered plate element is suggested to prevent buckling.