Abstract: To address the issue that the traditional well hydraulic models failed to reflect the clogging-induced permeability reduction and the deviation from Darcy’s law, a model for the groundwater hydraulics was developed for constant-rate injection tests (CRTs) and constant-head injection tests (CHTs) in confined aquifers using fully penetrating wells. In the model, a temporally decaying function of time was used for the clogging-related permeability reduction and the Izbash equation was adopted to describe the deviation from Darcy's law of groundwater flow. For the scenario when the clogging region coincides with the non-Darcian flow region, the approximate semi-analytical solution was derived using the linearization procedure and the Laplace transforms; while for scenarios where these regions do not overlap, a numerical solution based on the piecewise nonlinear Galerkin method was developed. A parametric study indicated that: In the CRTs, a smaller asymptotic hydraulic conductivity K_nd,∞ and a larger clogging scope r_c reduced the hydraulic head increment s in the clogging region and had no effect on flow dynamics in formation zone; whereas in CHTs, a smaller K_nd,∞ and a larger r_c reduced the s in both the clogging zone and the formation zone; a smaller n leads to smaller s in CRTs but larger s in CHTs and reduces the head difference between models considering and neglecting clogging effects. Besides, the clogging in well vicinity resulted in an obvious inflection point at r = r_c on the s-logr curve in both CRTs and CHTs and lead to an apparent decreasing stage of the s-logt curve. These features provide valuable insights for assessing and predicting the evolution of injection clogging.