Compressive and tensile properties of non-twisted and twisted carbon nanotube (CNT) bundles are studied using molecular dynamics (MD) simulations. The results reveal that non-twisted CNT bundles exhibit better compressive and tensile properties than twisted CNT bundles. When the twist angle of a CNT bundle is greater than 60°, its buckling load dropped considerably due to the significant curve geometries of the surrounding single-walled carbon nanotubes (SWCNTs). Twisted CNT bundles also do not demonstrate good tensile properties. During tensile loading, the intertube distance in CNT bundle with twisting angle greater than 75° will decrease as the strain increases. This gives rise to increasing intertube van der Waals forces until the intertube distance falls below 2.0Å. At this time, the repulsive force between the SWCNTs suddenly increases causing the SWCNTs to repel one another at junction areas where they overlap. As a result, twisted CNT bundles tend to fail at these junction areas with lower failure load and strain.