The occurrence of streaming potentials is directly related to movement of fluids in the subsurface. To investigate whether streaming potential measurements in boreholes and at the surface can be used to monitor subsurface flow and detect subsurface flow patterns in oil reservoirs, we model streaming potential responses caused by oil well pumping in monitoring wells and at the earth's surface. Since the model parameters: permeabilities, cross-coupling properties, and electric conductivities depend on a few basic rock-physics parameters such as brine conductivity, amount of water saturation, and porosity, the model parameters are evaluated self-consistently using rock-physics models. Using a threedimensional, (3-D) finite-difference algorithm, the governing differential equations that are drawn from nonequilibrium thermodynamics are solved numerically in three self-consistent steps: solution of the hydraulic problem, computation of the streaming current sources based on the principle of conservation of charge, and solution of the resistivity problem. For simple models of oil reservoirs at shallow depth between 325 m and 500 m, we assume a total production rate of 500 bbl/day for all phases (gas/water or oil/water), a porosity of 0.2 in the reservoir, brine conductivities in the range of 0.3 S/m to 1.0 S/m, and water saturations in the range of 0.7 to 1.0. Maximum values of the computed streaming potential response are less than 0.6 mV at the surface and less than 9 mV in the monitoring wells. The streaming potential response depends on brine conductivity, conductivity structure, well casing, and reservoir dimensions and decreases rapidly with distance from the production well. The parameterization of the models establishes bounds for the expected streaming potential response that varies by approximately one order of magnitude. Because of the ac nature of pumping processes, signal stacking could perhaps be used to make the expected small signals discernible. Our models are mainly limited by poor knowledge of in-situ, cross-coupling properties.