Abstract: The infinite-series solutions for the creeping motion of a viscous imcomperssible fluid from half-space to semi-infinite circular cylinder are presented. The results show that inside the cylinder beyond a distance equal to 0.5 times the radius of tube from the pore opening, the deviation of the velocity profile from the Poiseuille one becomes equal to or less than 1%.The inlet length in this case is considerably shorter than Dagan's finite circular cylinder one. In the half-space outside the cylinder pore the region, strongly affected by the tube wzll, is restricted within a narrow limit no more than one radius of the tube from the orifice. Beyond this region the solutions match almost exactly the Sampson's one for a flow through an orifice of Zero thickness, The relationship between the pressure drop and the volumetric flow rate is also considered in this paper.