The linear three-dimensional instability of the flow due to a low frequency traveling magnetic field in a regular cylinder is studied numerically for height-to-diameter ratios in the range [0.5:2.5]. The first instability has the form of an azimuthal wave with wave numbers between I and 6 depending on the aspect ratio. It is shown that the flow is stable if the Reynolds number is below 290. Even stronger stationary flows may be obtained in a flattened cylinder. (C) 2004 Elsevier B.V. All rights reserved.