To define the inner outline of a tunnel cross-section, a novel Wu’s two-parametric curve(heteromorphic ellipse)was proposed in this study, based on the iso-concentration curve equation of a conservative substance under the condition of steady point source from river center. The heteromorphic ellipse is a completely continuous and derivative-smooth curve, represented by the maximum height(H)and the maximum width(W)of the tunnel cross-section. Taking the compressibility factor θ=W/H as the criterion, the shape classification of H-type, Standard-type and W-type for the heteromorphic ellipse were given. The cross section, the theoretical calculation formula of water surface width, flow area, wetted perimeter, hydraulic radius and other hydraulic elements were deduced for the free-flow tunnel. The theoretical calculation formulas and curves for the velocity and the flow rates were found to be applicable to different specifications of the cross-section size, compressibility, roughness and gradient. Case studies show that the characteristic values of hydraulic elements have a high degree of anastomosis for the equivalent heteromorphic ellipse and the Ⅱ-type horseshoe(with chamfer)cross-section in a free-flow tunnel. Therefore, the proposed heteromorphic ellipse cross-section can be a novel application in water-conveyance tunnels with great academic research value.