Carbon nanotubes (CNTs) and their derivatives are allotropes of carbon that display outstanding physical properties including excellent thermal and mechanical properties, chemical inertness, and tuneable opto-electronic properties. Owing to these properties, CNTs are considered as an important research subject for scientists. Many investigations have been conducted to explore the properties of carbon nanostructures. The possible introduced defects applied to the structure of the CNTs include carbon vacancies, substitute dopant (e.g., silicon, boron, nitrogen), Stone-Wales pair defects, and so on. Structural are known to greatly affect the mechanical properties of CNTs and CNT-derived materials by reducing mechanical strength and structural stability of these structures. This chapter discusses the most recent studies concerning the mechanical properties of CNTs and CNT derivatives which are defect-free and those containing various types of defects.