Cleft lip and palate patients suffer from functional, aesthetical, and psychosocial problems due to suboptimal regeneration of skin, mucosa, and skeletal muscle after restorative cleft surgery. The field of tissue engineering and regenerative medicine (TE/RM) aims to restore the normal physiology of tissues and organs in conditions such as birth defects or after injury. A crucial factor in cell differentiation, tissue formation, and tissue function is mechanical strain. Regardless of this, mechanical cues are not yet widely used in TE/RM. The effects of mechanical stimulation on cells are not straight-forward in vitro as cellular responses may differ with cell type and loading regime, complicating the translation to a therapeutic protocol. We here give an overview of the different types of mechanical strain that act on cells and tissues and discuss the effects on muscle, and skin and mucosa. We conclude that presently, sufficient knowledge is lacking to reproducibly implement external mechanical loading in TE/RM approaches. Mechanical cues can be applied in TE/RM by fine-tuning the stiffness and architecture of the constructs to guide the differentiation of the seeded cells or the invading surrounding cells. This may already improve the treatment of orofacial clefts and other disorders affecting soft tissues.