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Strong effects of uniaxial and torsional strains on the magnetic properties of single-walled carbon nanotubes have been investigated by tight binding calculations and the Green function analyses. The strain-induced peaks of susceptibility are found in the carbon nanotubes, and paramagnetic-diamagnetic transition takes place at certain strains. The critical magnetic flux for semiconductor-metal transition changes linearly with strains depending on the chiralities of the tubes, mainly due to the tuning of the Van Hove singularities by the coupling of strains and magnetic flux. The positive and negative strain effects are asymmetrical in chiral tubes.