Mechanical stretch under both physiological (breathing) and pathophysiological (ventilator-induced) conditions is known to significantly impact all cellular compartments in the lung, thereby playing a pivotal role in lung growth, regeneration and disease development. In order to evaluate the impact of mechanical forces on the cellular level, in vitro models using lung cells on stretchable membranes have been developed. Only recently have some of these cell-stretching devices become suitable for air-liquid interface cell cultures, which is required to adequately model physiological conditions for the alveolar epithelium. To reach this goal, a multi-functional membrane for cell growth balancing biophysical and mechanical properties is critical to mimic (patho)physiological conditions. In this review, i) the relevance of cyclic mechanical forces in lung biology is elucidated, ii) the physiological range for the key parameters of tissue stretch in the lung is described, and iii) the currently available in vitro cell-stretching devices are discussed. After assessing various polymers, it is concluded that natural-synthetic copolymers are promising candidates for suitable stretchable membranes used in cell-stretching models. This work provides guidance on future developments in biomimetic in vitro models of the lung with the potential to function as a template for other organ models (e.g., skin, vessels).