Fully developed flow in a helical pipe is investigated with a view to modelling blood flow around the commonly non-planar bends in the arterial system. Medical research suggests that the formation of atherosclerotic lesions is strongly correlated with regions of low wall shear and it has been suggested that the observed non-planar geometry may result in a more uniform shear distribution. Helical flows driven by an oscillating pressure gradient are studied analytically and numerically. In the high-frequency limit an expression is derived for the second-order steady flow driven by streaming from the Stokes layers. Finite difference methods are used to calculate flows driven by sinusoidal or physiological pressure gradients in various geometries. Possible advantages of the observed helical rather than planar arterial bends are discussed in terms of wall shear distribution and the inhibition of boundary layer separation.