This paper reports on oriented poly(vinyl alcohol)/single-walled carbon nanotube (PVA/SWNT) tapes that were prepared by a mild processing route, involving the use of dimethyl sulfoxide (DMSO) as a solvent. Composite films with homogeneously dispersed SWNTs were cast from solution and drawn into oriented tapes using solid-state drawing. The obtained tapes showed the extraordinary reinforcing effects of the SWNTs, as the addition of 1.0 wt% SWNTs tripled the tensile strength of the PVA tapes. Micromechanical analysis showed that the nanotube contribution to the composite strength was as high as 88 GPa, which is very high when compared to other data reported in the literature, and for the first time begins to exploit the theoretical strength of nanotubes.