Bathymetry on continental hydrographic networks is up to now limited to small areas. This hampers exhaustive hydrological or ecological studies on hydrographic networks at management scales. To enlarge rivers bathymetry surveys, bathymetric, i.e. green LiDAR appears as an interesting tool. But if this technique has been widely used for coastal surveys, very few studies focus on water depth measurement quality and limits, in particular for rivers and for very shallow waters. We aimed here to assess the utility of LiDAR for bathymetry on rivers, in particular the minimum water depth Hinf we can theoretically measure with LiDAR, depending on LiDAR system and surface water characteristics. To meet this goal, we developed a LiDAR wavecform model depending on LiDAR parameters and introducing specificities for rivers (roughness and longitudinal slope for the water surface). Then, we assessed from a set of simulated full waveforms the inferior limit Hinf. In case of mean water surface roughness and no longitudinal slope, a minimum water depth of Hinf = 0.41 m has been found with the 95 % confidence interval [0.31, 0.45]. Some additional tests using different water surfaces rugosities show that a lowly significant rugosity optimum exists. These first results have to be experimentally validated then it could be extended to study the minimum water depth or depth measure quality sensitivities to LiDAR system and water surface parameters.