We solve the problem of magnetic field generation by a laminar flow of conducting fluid with helical (screw-like) streamlines for large magnetic Reynolds numbers, Rm. Asymptotic solutions are obtained with help of the singular perturbation theory. The generated field concentrates within cylindrical layers whose position, the magnetic field configuration and the growth rate are determined by the distribution of the angular, Ω, and longitudinal, Vz, velocities along the radius. The growth rate is proportional to Rm−½. When Ω and Vz are identically distributed along the radius, the asymptotic forms are of the WKB type; for different distributions, singular-layer asymptotics of the Prandtl type arise. The solutions are qualitatively different from those obtained for solid-body screw motion. The generation threshold strongly depends on the velocity profiles.