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Slug tests generating oscillating (underdamped) responses are common in high-transmissivity (T) zones, and the nature of the response depends on the plumbing of the test equipment and the formation properties. The standard approach for obtaining T is to measure pressure shallow in the riser pipe to obtain an accurate estimate of flow and then predict the formation response from this shallow measurement by accounting for friction and acceleration assuming steady flow conditions (parabolic radial velocity profile). In this study a mathematical solution is developed for unsteady oscillatory laminar flow that shows non-parabolic radial velocity profiles resulting in larger frictional losses, which are out of phase with the average flow velocity, indicating that errors are introduced when using the standard approach for underdamped slug test analysis. The unsteady flow model produces correction factors that can be used to improve the standard approach for predicting the formation pressure; however, not all errors are eliminated. Consequently, a new procedure is presented and applied to underdamped slug tests observed in fractured rock that avoids errors associated with quantifying inertial and frictional effects along the test equipment. This is achieved through the use of two transducers, where one is placed shallow in the water column to infer flow, and one is placed inside the test interval to represent the formation pressure. Comparison of T estimated by the new procedure to T derived from constant head step tests show better agreement than T obtained when predicting the formation pressure from a shallow pressure measurement.