Bending analysis of orthotropic super-elliptical plates of uniform thickness was investigated. Optimum location of the point supports was searched by minimizing the maximum absolute deflection. The support location which minimizes the bending moments at the supports was reported. The Ritz method was used and the total potential energy functional was modified by introducing the Lagrange multipliers to improve the accuracy of the stress resultants. The deflection and the bending moments computed at various points for a large variety of plate shapes ranging from an ellipse to a rectangle were checked with those of rectangular and elliptical plates. Good agreement was obtained for both cases. The structural response was found to be sensitive to support position.