Many articles have reported a correlation between the use of mechanical stimulation and an enhancement in cultivation of various tissues engineered in bioreactors. The enhancement includes improvements in cell growth, proliferation, and functionalities. The aim of this report is to review the mechanical functionalities of tissue engineering bioreactors in terms of the forms of stimulation, types of stress, actuators, supporting modules, and, most importantly, efficacy. The Google Scholar database was searched for relevant articles. Three forms of simulation were reported: uniaxial, biaxial, and multiaxial. The types of stress exerted by bioreactors include compression, tension, shear, and dynamic stresses, which are applied solely or mutually depending on the number of axes involved. Mechanical stimulation could be actuated by stepper motors, pistons, pneumatic pumps, diaphragm pumps, piezoelectric systems, or dielectric charges. Additional modules, such as incubators, flow perfusion systems, ultrasound sensors, movement controls, and electrodes, can also support the mechanical functions of bioreactors. The efficacy of a bioreactor could be determined by investigating the biomechanical and histological properties of the engineered tissues. To facilitate the development of mechanical functionalities for tissue engineering bioreactors in the future, a seven-step framework is proposed.