In this paper, we investigate the properties of frustrated three-leg spin tubes under a magnetic field. We concentrate on two kind of geometries for these tubes, one of which is relevant for the compound [(CuCl2tachH)3Cl]Cl2. We combine an analytical path integral approach with a strong coupling approach, as well as large-scale Density Matrix Renormalization Groups (DMRG) simulations, to identify the presence of plateaux in the magnetization curve as a function of the value of spin S. We also investigate the issue of gapless non-magnetic excitations on some plateaux, dubbed chirality degrees of freedom for both tubes.