The skeletal matrix of an aquifer is known to move laterally toward a discharging well. The mechanisms by which it moves relative to the well have been only partially studied in the past. Examining the relation of drawdown to volume strain for an assumed poroelastic solid has been a common approach. By way of contrast, the present study examines the relation of the velocity of solids (aquifer matrix) to their hydraulic driving forces. The present approach can be considered Darcian and allows the displacement field of the aquifer matrix to be calculated directly. A new formulation of the Darcy-Gersevanov law of water flowing relative to moving solids is applied to a Theis-Thiem confined aquifer. The aquifer is found to start with a maximum velocity when the pump is turned on and then to decelerate as time progresses. Dimensionless type curves of horizontal movement of the skeletal matrix are calculated. The resulting equation of aquifer deformation is checked against (1) results from alternatively using the standard poroelastic stress-strain approach and (2) the fundamental storage equation for transient groundwater flow.