Abstract We investigate the axisymmetric slow viscous flow around a sphere located on the axis of a long circular cylinder analytically based on the Stokes approximation. The sphere translates along the centerline of the cylinder with a constant velocity within Hagen–Poiseuille flow flowing far from the sphere. The translating velocity of the sphere and mean velocity of the Hagen–Poiseuille flow are arbitrary constant. To analyze Stokes equation, we use the method of complex eigenfunction expansions and the method of least squared error. As results, the streamline patterns and the pressure contour lines in the flow field are drawn for some radii of the sphere. The drag exerted on the sphere and the pressure change by the sphere are determined as the radius of the sphere. For a small sphere radius and for a sphere fitted closely in the cylinder, we compared results with previous asymptotic results and lubrication theory results, respectively. The velocity of the drifting sphere by the Hagen–Poiseuille flow in the circular cylinder is determined as the sphere radius. The pressure change induced by the drifting sphere in the Hagen–Poiseuille flow is also obtained. When the sphere translates along the plugged circular cylinder, a series of viscous toroidal eddies appears each side of the cylinder expectably. Moreover, we discussed the pressure and shear stress on the sphere surface and showed some critical range of these stresses.