In this paper, a numerical study is conducted to investigate the stress shadow effects (stress reorientation and change) during hydraulic fracturing in a transverse multiple fracture system. A numerical model is used for the numerical study. It is a 3D model and can simulate the fracture operation from injection begin to full closure (fracture contact). Therefore, there is no need to assume the fracture geometry for the investigation of the stress shadow effects (unlike previous studies). In the numerical study, the first and second operations in a fictive transverse multiple fracture system are simulated, meanwhile the stress shadow effects and their influences on the propagation and proppant placement of the second fracture are investigated. According to the results, the following conclusions are discerned: (1) most proppants are located in the lower part of the reservoir, even below the perforation; (2) the stress shadow effects are time-dependent and proppant dominated; (3) the stress shadow effects affect the fracture propagation and the proppant placement of the second fracture, and also the fracture conductivity of the first fracture; (4) the time-dependent stress shadow effects can be divided into four phases, fracture enlargement, closure without proppant contact, closure with proppant contact and full closure; and (5) the superposition effect of the stress shadow in a transverse multiple fracture system exists. According to the conclusions, some optimizations are recommended.