We quantitatively determine the effect and the uncertainty on solar neutrino production arising from the screening process. We present predictions for the solar neutrino fluxes and signals obtained with different screening models available in the literature and by using our stellar evolution code. We explain these numerical results in terms of simple laws relating the screening factors with the neutrino fluxes. Furthermore we explore a wider range of models for screening, obtained from the Mitler model by introducing and varying two phenomenological parameters, taking into account effects not included in the Mitler prescription. Screening implies, with respect to a no-screening case, a central temperature reduction of 0.5%, a 2% (8%) increase of Be-7- (B-8-) neutrino flux and a 2% (12%) increase of the gallium (chlorine) signal. We also find that uncertainties due to the screening effect are at the level of 1% for the predicted Be-7-neutrino flux and gallium signal, not exceeding 3% for the B-8-neutrino flux and the chlorine signal.