This paper presents new analytical solutions for steady state piezometric heads in phreatic and confined aquifers with radial flow. The new solutions utilize two constant head boundaries and a hydraulic conductivity k or thickness of aquifer H that is a linear function of radius r. Previous solutions applied constant k and H, and they were usually based on one constant head boundary, which might be superimposed on a solution that allowed a constant discharge or recharge at the center of the aquifer. The previous solutions may be difficult to apply to real aquifers because constant k and H is usually an oversimplification of nature. The Dupuit-Forchheimer assumption implies that vertical head gradients are ignored. The magnitude of the error introduced by allowing H = H(r) is evaluated numerically in this paper.