We investigate the “inverse” problem consisting in the determination of the transmissivity and the storativity of an aquifer in every point of a net. The equations of the problem are generally undetermined, and one is led to introduce smoothing conditions. We also consider other two types of constraints: the knowledge of the transmissivity and the storativity in a certain number of points, and prescribed regions of equal values. Finally, we have several different solutions according to the relative importance of each constraint, and according to the selected norm. We explicit these solutions in the case of the Euclidean norm; they can be expressed very simply by means of pseudo-inverses.