The concept of Functionally Graded Materials was proposed for severe environment application like space, thermal barrier coating etc. However, these materials had been successfully used in several fields of engineering. In these materials, properties of interest vary gradually from point to point. Understanding the fracture mechanics of these materials has been of interest to researchers to better utilize the capabilities of these materials and tailor the properties according to requirement. This work detail the fracture behavior of functionally graded material under in-plane and out-of-plane load. The numerical simulation and results of effects of material property variation on planar crack propagation have been presented. The numerical technique is based on spectral scheme.Several kinds of graded material have been considered. Along with the dynamic fracture, stationary crack embedded in inhomogeneous material has also been discussed. Finite element analysis of wave propagation in a bar of inhomogeneous material is discussed.