We investigate to what extent the radiation and stellar wind momenta in a massive close binary system can remove part of the matter flowing from one towards the other star during a mass transfer phase. We perform radiation-hydrodynamics simulations in the co-rotating frame of a binary system made-up of two main sequence stars of 27 M-circle dot and 26 M-circle dot in a 4 day orbit. We study the interaction of the winds of both stars, and of their photons, with the accretion stream originating from the Roche-lobe filling component. For our simulation, we adopt a mass transfer rate of 5x10(-6) M-circle dot yr(-1), a mid-point in the range of values during massive binary star evolution. Our simulations show that even for such moderate mass transfer rates, the wind and radiative momenta do not alter the dynamics of the accretion stream which is observed to follow essentially ballistic trajectories. Such a conclusion is reinforced for higher mass transfer rates because of the increased stream density and the correspondingly reduced radiation force. We anticipate that the radiation and wind momenta will affect the accretion stream only when its density is comparable to the wind's, a situation wherein the mass transfer rate is vanishingly small and irrelevant for binary star evolution. Alternatively, such reduced accretion stream density could be obtained from spatial dilution in wider systems, potentially leading to non-conservative mass transfer.