In this article, the achievement of a uniform elastic contact pressure in a frictionless, keyless, shaft-hub interference fit obtained by properly shaping the mating profiles is examined. The peculiarity of the hub mechanical response according to which, under the effect of a uniform pressure applied to the hub bore, the bore axial profile moves radially without any distortion, is exploited to simplify the determination of the mating profiles that return a uniform pressure. In particular, the hub radial deflection may be computed with a simple plane model, whereas only the shaft radial deflection requires a more complex analysis in cylindrical coordinates. Explicit approximate expressions are reported for the shapes to be conferred to the mating profiles to achieve a uniform pressure. Selected examples are presented to clarify the proposed design procedure and to preliminarily explore the effect on the pressure profile of simple shape errors.