This book is basically based on the Modeling and Numerical analysis of functionally graded materials. It mainly focused on the mechanical characterization of functionally graded polymer nanocomposites(FGPNCs). To enhance the application of FGPNCs in the field of aerospace, biomedical field, sports etc. The effect of nano-reinforcement, the effect of shape (spherical and rod particles) and orientation on mechanical properties of Functionally Graded Polymer Nanocomposites (FGPNCs) and Polymer nanocomposites (PNCs) with interphase has been investigated by using finite element method (FEM). Alumina has been taken as filler material and epoxy as the matrix. Nano samples were created by using MATLAB and whole analysis was done on ANSYS. For validation of ANSYS results, Mori-Tanaka (MT) method was used. It was found that the results obtained from FEM were in good agreement with the MT method. The further parametric study was done to see the effect of shape, weight fraction, and orientation of reinforcement on the effective flexural modulus of FGPNC and effective elastic modulus PNCs.