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In terms of a single-π orbital model, an analytical expression of the lowest-lying conduction-band and the highestlying valence-band is derived for single wall carbon nanotubes under both the uniaxial and torsional strains. We observe not only semiconductor-metal transitions in primary metallic tubes, but also insulator-metal transitions in semiconducting tubes. Additionally, an indirect transition of electrons and a quantized electron-resonance have been expected in optical spectrum experiments of the nanotubes.