Abstract: When a horizontal well is transversally fractured with multiple stages, initial crack can induce the secondary change of the wellbore stress, producing the induced stress ield which has an inluence on subsequent crack initiation. Based on the elasticity and tensile failure theory, this paper develops a stress distribution model around wellbore and a theoretical model for calculating the break- down pressure. The results show that size and distribution of induced stress depend on crack spacing, fracture height and in-situ stresses. The induced stress decreases along wellbore direction with the increase of crack spacing; when crack spacing is ixed, breakdown pres- sure increases as fracture height rises; in-situ stress distribution is independent with breakdown pressure change in induced stress ield, which only determines the increase amplitude of breakdown pressure. This result can be used to guide optimization design of staged fracturing for horizontal wells.