A three-body model for the deuteron stripping nuclear reactions is presented. A set of three integral equations is obtained for the wave functions of the three-body problem by introducing a decomposition into angular momentum states into the Lippmann-Schwinger equation. Simple two-particle interactions with separable potentials are used. These separable potentials reduce the three-body problem to the solution of coupled sets of one-dimensional Fredholm integral equations. The angular distributions for28Si(d,p)29Si and40Ca(d, p)41Ca stripping reactions are calculated. From the extracted spectroscopic factors, good agreement with the experimental measurements is obtained.