We investigate the spin-transfer torque in a magnetic multilayer structure by means of a spin-diffusion model. The torque in the considered system, consisting of two magnetic layers separated by a conducting layer, is caused by a perpendicular-to-plane current. We compute the strength of the field-like and the damping-like torque for different material parameters and geometries. Our studies suggest that the field-like torque highly depends on the exchange coupling strength of the itinerant electrons with the magnetization both in the pinned and the free layer. While a low coupling leads to very high field-like torques, a high coupling leads to low or even negative field-like torques. The dependence of the different torque terms on system parameters is considered very important for the development of applications such as STT MRAM and spin-torque oscillators.