We have developed a drawdown solution for a partially penetrating well under constant flux pumping in a confined aquifer with finite thickness. The predictions of our solution diverge from the predictions of Hantush's solution (1961), particularly for problems with low ratios of well screen length to aquifer thickness. Furthermore, the predicted drawdown from Hantush's solution (1961) differs from that of Yang et al.'s solution Water Resour Res 42:W0552, (2006) only near the well and at small time values as indicated in Yang et al. Water Resour Res 42:W0552, (2006). Our solution is based on Green's function with a columnar source (sink) that represents pumping from a finite-radius well. Hantush's solution (1961) and Yang et al.'s solution Water Resour Res 42:W0552, (2006), however, were derived from Laplace transform techniques for pumping in a well with an infinitesimal and a finite radius, respectively.