We investigate the properties of nanotubes obtained from recently described boron alpha-sheet, using density functional theory. Computations confirm their high stability and identify mechanical stiffness parameters. This allows one to further analyze the basic vibrations, including the radial breathing mode Raman frequency, fRBM = 210(nm/ d) cm (-1). Careful relaxation reveals the curvature-induced buckling of certain atoms off the original plane. This distortion changes the overlap of the orbitals near the Fermi level and opens up the gap in narrow tubes, rendering them semiconducting. Wider tubes with the diameter d greater, similar 1.7 nm retain original metallic character of the alpha-sheet. This combination of properties could make boron alpha-tubes (BT) an important material for electronic, bio- and chemical sensing, and optical applications.