(PRB,74,245428,2006) Based on a molecular mechanics concept, a nonlinear stick-spiral model is developed to investigate the mechanical behavior of single walled carbon nanotubes (SWCNTs). The model is capable of predicting not only the initial elastic properties (e.g., Young’s modulus) but also the stress-strain relations of a SWCNT under axial, radial, and torsion conditions. The elastic properties, ultimate stress, and failure strain under various loading conditions are discussed and special attentions have been paid to the effects of the tube chirality and tube size. Some unique mechanical behaviors of chiral SWCNTs, such as axial strain-induced torsion, circumferential strain-induced torsion, and shear strain-induced extension are also studied. The predicted results from the present model are in good agreement with existing data, but very little computational cost is needed to yield them.