Many models were offered in the literature to simulate the material gradation patterns within the functionally graded metal-ceramic structures. The present study provides a comprehensive and comparative numerical examination of the displacement and stress distributions in the three types of annular structures, namely spheres, cylinders, and annuli by gathering most of models up. To this end, an efficacious and accurate numerical method, the complementary functions method, is exploited in the numerical determination of the elastic fields with several material-grading patterns under internal pressure including centrifugal forces to search the best one exhibiting desired elastic axisymmetric behavior of such structures. A functionally graded material, viz., a particle reinforced composite, is assumed to be composed of an aluminum oxide (ceramic/Al2O3) and a stainless steel (metal/SUS-410). Different grading patterns are formed by using several material grading rules such as a simple power rule, an exponential rule, a linear function, a Voigt mixture with power of volume fractions of constituents, a Mori-Tanaka scheme, Chung and Chi's Sigmoid function, Chen and Lin's sine rule, Dryden and Jayaraman's combined power and exponential rule, and finally Tornabene's four-parameter symmetric/asymmetric power functions. Variation of the elastic fields is presented in both tabular and graphical forms. Combined effects of both the pressure and rotation are also studied for cylinders and annuli having aspect ratios of 0.6 and 0.9. It is observed in the chosen patterns that a pattern with gradually increasing ceramic constituents toward a full ceramic layer at the outer surface is found as the best under pressure loads. Combined pressure plus centrifugal forces require a pattern having a full ceramic layer at the inner surface following a decreasing pattern with ceramic constituent toward the outer surface. The results with plain stress assumption are found somewhat higher than the results with generalized plane strain. As expected, the spheres have significantly smallest elastic fields than the others under the same pressure loads and aspect ratios.