Functionally graded materials (FGMs) are widely used in engineering applications for the advantages offered by the properties of materials in combination. It is a special type of composite material which is inhomogeneous (micro-scopically). Laser cutting offers advantages while cutting these materials compared to traditional cutting methods. The objective of this work is to investigate numerically the effect of process parameters such as laser power and scanning speed on kerf width, depth of cut and thermal stress. Gaussian heat source, representing the laser beam, is applied along a straight line path through the middle of the work piece. The FGM considered in this work material mainly consists of a FGM made of nickel and stainless steel (AISI 304). The work piece is assumed to be symmetric. In this simulation finite element software COMSOL MULTIPHYSICS is used to simulate the thermo-mechanical model. The model is meshed with nonuniform pattern tri-angular mesh. It is observed from the results of numerical simulation that with the increase of laser power the width and depth of the cut has increased. The cut has a very narrow kerf width with increasing scanning speed leading to considerable saving in material. The variation in thermal stress is observed on the material with the considered parameters.