Variable-head permeability tests are performed in monitoring wells (MWs) or open holes between packers to assess the local value of hydraulic conductivity, K, of gravel, sand, and fractured rock. This article examines physical reasons for having an oscillating water level in the riser pipe, called underdamped (UD) response. The UD solutions are incomplete because they solve one half of the problem—for the water in the pipe—and ignore the second half, seepage in the tested material. This article shows that these half-solutions violate mathematical rules for the second half and thus, are incorrect. Four reasons for oscillations are examined: (1) solid matrix elasticity (storativity), (2) trapped gas, (3) sealing defect, and (4) hydraulic fracturing. Reason (1) yields small oscillations but not large oscillations. Reasons (2–4) can yield large oscillations and explain field data for occurrence, frequency, and damping. Thus, a free space along the casing or some trapped gas is needed to observe large oscillations. Hence, a UD slug test response only proves that the MW (or a packer) is poorly installed. This MW yields wrong values for hydraulic head, gradient, and water analyses. The data of oscillating slug tests are shown to depend upon parameters that are not easy to evaluate. This is why the UD slug tests are found to give poor estimates of K. It is recommended to use suitable drilling techniques to avoid overexcavation, to take 2–4 hours to correctly install a MW, to avoid using compressed gas to start a slug test, and to apply head differences that are high enough to have good results but lower than those producing hydraulic separation. For packer tests, it is recommended to monitor the water pressure between the packers, in the hole below the lower packer and above the upper packer, using three pressure sensors.
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