The applicability of the Theis-formula (1935) and the Jacob-Hantush leakage-formula (1946 and 1956) as tools for the description of water-level variations due to pumping from artesian aquifers, is shown to be rather limited, especially in long term pumping situations. The limitations are discussed and illustrated through a review of some mathematical models with more reliable and physical realistic preconditions, and a general perception of the physics governing the drawdowns in pumping from leaky artesian aquifers is hereby established. Data from 10 years of heavy pumping from a leaky artesian multi-aquifer at Egebjerg near Horsens, Denmark, are analysed, and the result turns out to be in good agreement with the theoretical discussion.