Abstarct: On this thesis, the stress intensity factor of mode I in a edge cracked plate or a cylindrical which is contains a circumferential or semi-elliptical crack is extracted by using the weight function method. the plate and cylinder which are made of thermoelectric material such as bismuth telluride are subjected to the Non-fourier thermal shock according to the cattaneo- vernotte as well as dual- phase lag madels. In order to extract the result, the Non- fourier heat conduction problem is solved in laplace domain at the first. Also, the stress distribution is obtained in laplace domain, the time variation of the stress distribution is by using numerical laplace inversion methods at last. The stress intensity factor are obtained by using the weight function method. The effect of Joule and Thompson coefficients on the results are investigated