Abstarct: A unified modeling and analysis approach to address the functionally graded plane and Axisymmetric problems is suggested which is making use of B-Splines and NURBS for the definition of geometry and material properties as well as the analysis and optimization. The recently developed Isogeometric Analysis numerical method is concisely explained and the functionally graded materials (FGMs) are briefly introduced. FGMs are composite materials that are microscopically homogeneous but at macro level the mechanical properties vary continuously from one point to another by smoothly varying the volume fractions of the material constituents. The constitutive material matrix is considered to be isotropic at each point where the elastic modulus is assumed to vary continuously throughout the domain according to an assumed arbitrary distribution. It is shown that the difficulties encountered in the Finite Element analysis of the FGMs are to a large degree alleviated by employing the Generalized Isogeometric Analysis which is the subject of this thesis. Finally, examples are presented to demonstrate the efficiency of the method.