Different models for the calculation of residual stresses induced by cooling down from elaboration process in SiC/Ti-15-3 composite were presented. First of all, an analytical model (derived from those of Eshelby and of Mikata and Taya) already used for ceramic matrix composites is explained. It is a suitable method for elementary composites but we present an extension of this model to real (1D) composites. Then, we also briefly present the finite model using MARC and MENTAT softwares. Finaly, an analytical model to predict the evolution of TRS during a fatigue test is detailed. The part II of the paper will present the results obtained using all these differents models.