In this work, element free Galerkin method (EFGM) has been used to obtain the solution of various edge crack problems under thermo-mechanical loads as it provides a versatile technique to model stationary as well as moving crack problems without re-meshing. Standard diffraction criterion has been modified with multiple crack weight technique to characterize the presence of various cracks in the domain of influence of a particular node. The effect of crack inclination has been studied for single as well as two edge cracks, whereas the cracks interaction has been studied for two edge cracks lying on same as well as opposite edges under plane stress conditions. The values of mode-I and mode-II stress intensity factors have been evaluated by the interaction integral approach.