For poly-crystalline semiconduetor film deposited on an insulator and then recrystallized by a laser beam, the influence of the substrate upon recrystallization of the film was analyzed theoretically. We found the critical laser power necessary for solid-liquid phase transition to take place, will change to a lower value as the poor thermal conduction of insulating substrate being reasonably considered. It is well known that the existence of stress in recrystallized films may be taken as a criterion for melting process that undergoes during laser lrradiation. A large number of SOI samples prepared by LPCVD technology were studied after its laser recrystallization, to obtain the critical transition conditions through strass determination by use of Raman peak shifts. A comparison of the calculations based on the model taking low thermal conductance of the substrate into account with the experimental results showed its fitting is better than that with the influence of substrate being neglected.