Physical solutions for the flow through circular channels due to increase in bed elevations are obtained, satisfying the condition of choke-free flow. In this analysis, three different cases of channel transitions, commonly found in practice, are considered. They are (1) when the channel bed is raised with the formation of a flat base; (2) when the channel bed is raised due to change in position of the centerline; and (3) when the channel bed is raised due to decrease in channel diameter. Considering a smooth and gradual transition zone, the equations of energy and continuity are solved for the subcritical approaching flow regime to determine the maximum limiting rise in bed elevation. Using the continuity equation of the upstream flow, the ranges of the upstream flow depths are also obtained for the choke-free condition.