The dependence of the mechanical characteristics of single-walled carbon nanotubes on their length, radius, and chirality is investigated by molecular dynamics simulation. The observed changes in the mechanical properties with radii are compared with the results reported by other authors under both tensile and compressive loading. The tensile properties of zigzag and armchair CNTs are not dependent on their lengths. Slight changes in the mechanical properties with chirality are also reported. However, their compressive properties, primarily their stiffness and critical compressive stress, vary with length for all types of CNTs. The fracture patterns show different modes in each case. Buckling produces kinks, wavy structures, shell-wall buckling, columnar buckling, bending, and twisting.