The low Reynolds number flow in a tube with helically corrugated wavy wall is solved for the first time. The Navier-Stokes equations are perturbed using the small wavy amplitude as parameter. For given pitch A there exists an optimum number of circumferential waves n where the resistance is minimum. For given n there exists an optimum A where the induced axial rotation of the flow is maximum. (c) 2006 American Institute of Chemical Engineers.