The band structures of fully hydrogenated Si nanosheets and nanotubes are elucidated by the use of an empirical tight-binding model. The hydrogenated Si sheet is a semiconductor with an indirect band gap of about 2.2 eV. The symmetries of the wavefunctions allow us to explain the origin of the gap. We predict that, for certain chiralities, hydrogenated Si nanotubes represent a new type of semiconductor, one with coexisting direct and indirect gaps of exactly the same magnitude. This behavior is different from that governed by the Hamada rule established for non-hydrogenated carbon and silicon nanotubes. A comparison to the results of an ab initio calculation is made.