A new path independent J-integral is derived to study the behaviour of the crack under the thermal shock and is calculated by the finite element method. For the validity of J-integral numerical analysis and experiments are undertaken. Summary of the research results is following: 1. J integral is expressed in the form of line integral by using the convolution integral. 2. Under Mode I thermal shock loading, the effect of inertia term on the J-integral value is not negligible for a glass plate but for steel plate. 3. Good agreement of fracture times predicted with the present J integral and measured with thermocouple is obtained for glass plate under Mode I thermal shock.