In an open channel, an emergent canopy of vegetation enhances local resistance, producing a complicated velocity distribution within and around the canopy. Laboratory experiments were performed to understand the flow velocity variations in a partially vegetated channel, revealing both streamwise and lateral velocity variations as the flow entered the canopy. An analytical model was proposed to predict the lateral velocity profiles across the vegetated region and bare channel in both the flow adjustment region and the fully developed flow region. The flow velocity variations in the streamwise and lateral directions were parameterized and included in the new proposed model, allowing the model to capture both the streamwise and the lateral velocity variations. Twenty sets of experimental data from our experiments and data from published studies were used to verify the new model. The predicted velocity profiles exhibited good agreement with the measurements under a wide range of vegetation and flow conditions, suggesting that the proposed model is capable of accurately predicting the velocity profiles in a partially vegetated channel. Finally, the proposed model was applied to evaluate the critical frontal area per canopy volume at which Kelvin–Helmholtz vortices form along the emergent canopy side edge. With the same spatially averaged velocity, the critical frontal area exhibited no dependence on stem diameter.