This review focusses on introducing the mechanics in carbon nanotubes (CNT), and the major applications of CNT and its composites in biomedicine. It emphasizes the nanomechanics of these materials by reviewing the widely followed experimental methods, theoretical models, simulations, classification, segregation and applications the aforementioned materials. First, several mechanical properties contributing to the classification of the CNT, for various biomedicine applications, are discussed in detail to provide a cursory glance at the uses of CNT. The mechanics of CNT discussed in this paper include: elasticity, stress, tension, compression, nano-scale mechanics. In addition to these basic properties, a brief introduction about nanoscale composites is given. Second, a brief review on some of the major applications of CNT in biomedicine including drug delivery, therapeutics, diagnostics and regenerative medicine is given.