For an efficient restoration of ecological continuity, rock-ramp fishways with protruding blocks and lateral slope can allow to conciliate two opposite objectives: sufficiently low flow velocities in some parts of the ramp for fish passage and a large global discharge for attractiveness. Flows in such ramps with several lateral slopes (from 5% to 18.5%), longitudinal slopes (from 1% to 7%) and discharges were investigated experimentally on a one-fifth scale model and numerically with RANS and LES models, to check up their passability compared to ramps with no lateral slope. Results revealed that the methodology for assessing stage-discharge relationship and maximum velocities is still relevant whatever the lateral slope. However, as the lateral slope increases, so does the lateral deviation of the free surface, as well as the transverse and vertical velocities in the emergent part of the ramp, near the submerged part. This is why it appears preferable to limit the transversal slope to a maximum 12% in rock-ramp fishways with protruding blocks. This recommendation is already much higher than the one applied up to now in France (lower or equal to the longitudinal slope, so mostly lower or equal to 4% to 6%) and will allow to reduce the width and thus the cost of the ramp. Highlights • CFD simulation with LES is pertinent to investigate flow in rock-rampfishway with a transversal slope and protruding blocks either emergent orsubmerged. • Lateral slope up to 12% do not disturb flow in the part where blocks areemergent, which makes it possible to consider lower build-cost fishway.