In this paper we numerically simulate flow in a helical tube for physiological conditions using a co-ordinate mapping of the Navier–Stokes equations. Helical geometries have been proposed for use as bypass grafts, arterial stents and as an idealized model for the out-of-plane curvature of arteries. Small amplitude helical tubes are also currently being investigated for possible application as A–V shunts, where preliminary in vivo tests suggest a possibly lower risk of thrombotic occlusion. In-plane mixing induced by the geometry is hypothesized to be an important mechanism. In this work, we focus mainly on a Reynolds number of 250 and investigate both the flow structure and the in-plane mixing in helical geometries with fixed pitch of 6 tube diameters (D), and centerline helical radius ranging from 0.1D to 0.5D. High-order particle tracking, and an information entropy measure is used to analyze the in-plane mixing. A combination of translational and rotational reference frames are shown to explain the apparent discrepancy between flow field and particle trajectories, whereby particle paths display a pattern characteristic of a double vortex, though the flow field reveals only a single dominant vortex. A radius of 0.25D is found to provide the best trade-off between mixing and pressure loss, with little increase in mixing above R = 0.25D, whereas pressure continues to increase linearly.