A formulation of stripping reactions into the continuum is given taking the(d, p)-reaction as a specific example. We use the DWBA and the assumption that contributions from the nuclear interior are negligible. Under these assumptions we show that the cross section can be split into a “distortion matrix element” and a term depending on the neutron target interaction only through the phase shifts of the corresponding elastic neutron scattering. The interference with the “pure break-up” process is discussed. The connection between stripping to bound and unbound states in the limit of zero binding energy is established. A comparison with recent experimental results is given, where the “distortion matrix elements” are calculated, for the sake of simplicity, in the “Butler approximation”.