Construction of a conveyance tunnel through rock often induces the ingress of groundwater into the tunnel, a flow that changes both the hydrogeological regime of the tunnel and its environment. To explore this key interaction, a novel modeling approach using the conduit flow process (CFP) is developed that considers both the hydraulic head and the ingress of water from the rock matrix during excavation. The resulting flow values are predicted through an adapted MODFLOW numerical model into which the tunnel is introduced with the aid of the new CFP approach. The CFP approach can simulate both laminar and turbulent flow in the tunnel whether the flow is free surface or pressurized. Several simulations, including one for which the permeability of the tunnel perimeter is assumed to be identical to the hydraulic conductivity of the surrounding rock matrix, are then used to explore the sensitivity of the predicted head and flow conditions to the permeability of the tunnel perimeter. Comparisons of the numerical results with field data from the Kerman Water Conveyance Tunnel in Iran show that the proposed approach accurately predicts the spatial variation of both groundwater ingress and hydraulic head.