This paper investigates symmetrical buckling of orthotropic circular and annular plates of continuous variable thickness. Uniform compression loading is applied at the plate outer boundary. Thickness varies linearly along radial direction. Inner edge is free, while outer edge has different boundary conditions: clamped, simply and elastically restraint against rotation. The optimized Ritz method is applied for buckling analysis. In this method, a polynomial function that is based on static deformation of orthotropic circular plates in bending is used. Also, by employing an exponential parameter in deformation function, eigenvalue is minimized in respect to this parameter. The advantage of this procedure is simplicity, in comparison with other methods, while whole algorithm for solution can be coded for computer programming. The effects of variation of radius, thickness, different boundary conditions, ratio of radial Young modulus to circumferential one, and ratio of outer radius to inner one in annular plates on buckling load factor are investigated. The obtained results show that in plate with identical thickness, increasing of outer radius decreases the buckling load factor. Moreover, increase of thickness of the plates results in increase of buckling load factor.