To contribute to the existing knowledge of thehydrodynamic force exerted on a spherical particle placed in theaxis of a cylinder, at small Reynolds numbers, the influence ofthe uniform and Poiseuille flows on the wall correction factor arenumerically and asymptotically investigated. The Stokes andcontinuity equations are expressed in the stream function andvorticity formulation and are rewritten in an orthogonal system ofcurvilinear coordinates. These equations are solved using afinite differences method. The generation of the grid was carriedout by the singularities method. The accuracy of the numericalcode is tested through comparison with theoretical andexperimental results. In both cases we numerically calculated theseparate contributions of the pressure and viscosity forces. Inconcentrated regime these numerical calculations are in very goodagreement with those obtained by asymptotic expansions. Thisanalysis allowed us to show the prevalence of the pressure termover the viscosity one in the lubrication regime contrary to whathappened for the dilute regime. All our numerical and asymptoticalresults compared with those of Bungay et al. (Int. J. Multiphase Flow 1, 25–56 (1973)) seem to give a response to this problem argued for a long time.