An analysis of the hydraulic entry-length problem in concentric annuli has been made by the linearized finite-difference method and the results are reported in this Note. Fifteen annuli of radii varying in ratio between 0.05 and 0.955 were investigated and typical radial velocity profiles at various axial distances from the annulus entrance are presented. A means for determining the pressure drop in the entry region is included. In the course of the study the developing axial profiles were observed to be in agreement with results in the literature.