An analytical solution for the non-inertia wave model is presented for a lateral inflow that is uniformly distributed between any two locations. The model is solved by using the Laplace transform. A stage-discharge relation is taken at downstream boundary, and the upstream boundary is either water-depth based or flow rate based. The flow rate responses for the positions between the lateral inflow boundaries are found to be dependent on the location of observation, which is not the case for the positions downstream and upstream of the lateral inflow boundaries. The backwater effect induced by the lateral inflow is observed in the flow rate as well as the water depth, irrespective of the type of upstream boundary. For a flow rate hydrograph imposed at the upstream section, the flow rate and water-depth responses for the locations downstream to the location of lateral inflow are independent to the location of lateral inflow in contrast to the case of a water-depth hydrograph at the upstream section.