The inverse weir problem, that of determining the weir shape in a thin plate weir to comply with a given headdischarge equation is known to depend on the solution ofintegral equation. This has been analytically solved in the past through a reduction to Abel's integral equation, when the discharge law is of the exponential type. Two simple and general numerical solutions to this equation are suggested and their results compared with a number of well known cases from the literature. The numerical method is then applied to the calculation of control weirs for open channels and sedimentation basins.