Abstract: In order to research on the effect of threshold pressure gradient and stress sensitivity on shale oil well productivity,a mathematical model that takes into consideration of the threshold pressure gradient and stress sensitivity for shale oil seepage was developed on the basis of oil-gas-water three-phase seepage model.A numerical solution method was offered and numerical simulator of shale oil reservoir was compiled.Patterns and mathematical rules for threshold pressure gradient and stress sensitivity on horizontal well productivity of multistage fracturing shale oil reservoir were analyzed by using a shale oil reservoir numerical simulator.The calculation results on the degradation of the simulator were basically identical with Eclipse software calculation results,which validated the correctness of the simulator.The numerical simulation results showed that the cumulative oil production rate for 10 000 days was 24.7% of that where there was no threshold pressure gradient when threshold pressure gradient reached 0.5 MPa/m. When the stress sensitivity coefficient rose from 0.1 MPa-1 to 0.5 MPa-1,the reservoir permeability near borehole zones dropped approximately one order of magnitude and the cumulative oil production rate was 36.2% that of no stress sensitivity effect after 10 000 days’ production.Moreover,the cumulative oil production was lower while simultaneously considering threshold pressure gradient and stress sensitivity effect.The results showed that the threshold pressure gradient and stress sensitivity effect both greatly inhibited shale oil productivity and the shale oil productivity might be overestimated without consideration of the threshold pressure gradient and stress sensitivity effect.Therefore a shale oil reservoir numerical simulator can provide guidance for the development of shale oil reservoirs.