Resonance Raman spectra of individual strained ultralong single-wall carbon nanotubes (SWNTs) are studied. Torsional and uniaxial strains are introduced by atomic force microscopy manipulation. Torsional strain strongly affects the Raman spectra, inducing a large downshift in the E2 symmetry mode in the G+ band, but a slight upshift for the rest of the G modes and also an upshift in the radial breathing mode (RBM). Whereas uniaxial strain has no effect on the frequency of either the E2 symmetry mode in the G+ band or the RBM, it downshifts the rest of the G modes. The Raman intensity change reflects the effect of these strains on the SWNT electronic band structure.