The problem addressed in this paper is the elastic local buckling of thin-walled compression members whose plate components are tapered in thickness along the longitudinal direction. In the design of structural system in construction, shipbuilding, and aerospace industries, such structural plate components are frequently encountered. The elastic buckling analysis of transversely isotropic plates with varying thickness and various boundary conditions is performed to derive the buckling equation of thin-walled members composed of tapered plate components. In the analytical solution, the energy approach is adopted. The analytical results are presented in a graphical form in which the plate buckling coefficients are suggested with respect to the width ratio of plate elements and the degree of taper. In addition, using the buckling equations of plates with specific boundary conditions, the simplified form of equation for the local buckling coefficient of structural members such as L-section, T-section, and Box-section is suggested.