The temperature and loading-rate dependence on the mechanical behavior of single-walled carbon nanotubes under axial compression and torsion is examined with classical molecular dynamics simulation. The critical buckling is found to depend on the temperature and loading-rate. The yielding under torsion is also found to depend on the temperature and loading-rate. But it is shown that the compression and torsional stiffness are independent of the varied temperatures and loading-rates.