Water surface elevation (WSE), slope and width measurements from the forthcoming Surface Water and Ocean Topography (SWOT) mission will enable spaceborne estimates of global river discharge. WSE will be measured by interferometric synthetic aperture radar (InSAR). InSAR measurements are vulnerable to contamination from layover, a phenomenon wherein radar returns from multiple locations arrive at the sensor simultaneously, rendering them indistinguishable. This study assesses whether layover will significantly impact the precision of SWOT estimates of global river discharge. We present a theoretical river layover uncertainty model at the scale of nodes and reaches, which constitute nominal 200 m and 10 km averages, respectively, along river centerlines. The model is calibrated using high-resolution simulations of SWOT radar interaction with topography covering a total of 41,233 node observations, across a wide range of near-river topographic features. We find that height uncertainty increases to a maximum value at relatively low values of topographic standard deviation and varies strongly with position in the swath. When applied at global scale, the calibrated model shows that layover causes expected height uncertainty to increase by only a modest amount (from 9.4 to 10.4 cm at the 68th percentile). The 68th percentile of the slope uncertainty increases more significantly, from 10 to 17 mm/km. Nonetheless, the 68th percentile discharge uncertainty increases only marginally. We find that the impact of layover on SWOT river discharge is expected to be small in most environments