his paper investigates the variations of mode I stress intensity factor (KI) for inner penny-shaped and circumferential cracks in functionally graded solid and hollow thick walled cylinders, respectively with the changes of crack geometry, material gradation and loading conditions. The functionally graded material of cylinders consists of epoxy and glass. It is assumed that the mechanical properties vary with a power law in the radial direction of cylinders. Micromechanical models for conventional composites are used to estimate the material properties of functionally graded cylinders. The equations of motion obtained from the extended finite element discretization are solved by the Newmark method in the time domain. The interaction integral method is employed to calculate the mode I stress intensity factor (KI). The MATLAB programming environment was implemented to solve the problem.