The interest to functionally graded materials (FGM) and structures has been generated by their potential advantages, including enhanced thermal properties, reduced or eliminated delamination concerns, a potential for an improved stress distribution, etc. Various aspects of the processing, design, micromechanics and analysis of FGM have been outlined in a number of reviews, mentioned here are [1-3]. In particular, functionally graded panels may be advantageous compared to their conventional counterparts in numerous applications. However, a typical FGM panel is asymmetric about its middle plane resulting in lower buckling loads and fundamental frequencies as well as higher stresses and deformations than the counterpart with a symmetric distribution of the same constituents. The reduced stiffness of FGM panels can be compensated by reinforcing them with stringers. For example, metallic stringers at the metal-rich surface of a FGM ceramic-metal panel may provide an efficient solution enabling a designer to increase both buckling loads as well as natural frequencies. The list of studies on optimization of FGM is extensive as could be anticipated for such tailored structural elements. For example, recent papers by Batra and his collaborators present optimization of the natural frequencies of a FGM plate through material grading [4] and through the graded fiber orientation [5]. The present paper is concerned with an optimum design of the system of stringers for a specified FGM panel. The task is to design the lightest system of stringers enabling the panel to achieve prescribed buckling loads or fundamental frequency.