In H shape rolling, accurate predictions of deformation and temperature distribution in a billet are quite important because they are the main factors in determining roll calibers and roll pass schedules. Many researches have been performed to achieve the predictions, but most of them are limited to single pass or isothermal assumptions. In the present investigation, it is attempted to develop a method to predict the deformation and temperature distributions which is applicable to a complete rolling process that usually consists of several rollings under different rolls for a period of time. The method works by coupling two analyses : one is an approximate analysis for temperature distribution prediction and the other is the slab-FEM hybrid analysis for deformation prediction. The method is applied to analyze a "H" shape rolling process consisting of nine passes under four different rolls. In the present paper, basic ideas of the method are presented. Also, shapes of cross sections, strain and temperature distributions, roll separating force and roll torque predicted by the method are discussed.