Understanding how changes in the groundwater table affect surface water resources is of fundamental importance in quantitative hydrology. If the groundwater table below a stream is sufficiently deep, changes in the groundwater table position effectively do not alter the infiltration rate. This is referred to as a disconnected system. Previous authors noted that a low-conductivity layer below the surface water body is a necessary but not sufficient criterion for disconnection to occur. We develop a precise criterion that allows an assessment of whether surface water–groundwater systems can disconnect or not. We further demonstrate that a disconnected system can be conceptualized by a saturated groundwater mound and the development of a capillary zone above this mound. This conceptualization is used to determine the critical water table position at the point where full disconnection is reached. A comparison of this calculated critical water table position with a measurement of the water table depth in a borehole allows the assessment of the disconnection status. A sensitivity analysis of this critical water table showed that for a given aquifer thickness and river width, the depth to groundwater where the system disconnects is approximately proportional to the stream depth and the hydraulic conductivity of the streambed sediments and inversely proportional to the thickness of these sediments and the hydraulic conductivity of the aquifer. The conceptualization also allows the disconnection problem to be analyzed using both variably saturated and fully saturated groundwater models and provides guidance for numerical and analytical approaches.