In this paper, some functionally gradient elements of extensive engineering interest including plates, beams, cylinders and thick-walled tubes are theoretically investigated. First, some elastic analytical solutions are derived for such components made of functionally graded materials (FGMs) under different loadings, and the effective elastic properties are formulated in explicit expressions. These solutions are compared to the conventional composite models in micromechanics, and thereby some interesting conclusions are obtained. Then, the above elements are investigated, based on the theory of plasticity. The results are useful for design and analysis of FGMs-based structures and for optimization of FGMs.