Skin is a highly dynamic, autoregulated, living system that responds to mechanical stretch through a net gain in skin surface area. Tissue expansion uses the concept of controlled overstretch to grow extra skin for defect repair in situ. While the short-term mechanics of stretched skin have been studied intensely by testing explanted tissue samples ex vivo, we know very little about the long-term biomechanics and mechanobiology of living skin in vivo. Here we explore the long-term effects of mechanical stretch on the characteristics of living skin using a mathematical model for skin growth. We review the molecular mechanisms by which skin responds to mechanical loading and model their effects collectively in a single scalar-valued internal variable, the surface area growth. This allows us to adopt a continuum model for growing skin based on the multiplicative decomposition of the deformation gradient into a reversible elastic and an irreversible growth part. To demonstrate the inherent modularity of this approach, we implement growth as a user-defined constitutive subroutine into the general purpose implicit finite element program Abaqus/Standard. To illustrate the features of the model, we simulate the controlled area growth of skin in response to tissue expansion with multiple filling points in time. Our results demonstrate that the field theories of continuum mechanics can reliably predict the manipulation of thin biological membranes through mechanical overstretch. Our model could serve as a valuable tool to rationalize clinical process parameters such as expander geometry, expander size, filling volume, filling pressure, and inflation timing to minimize tissue necrosis and maximize patient comfort in plastic and reconstructive surgery. While initially developed for growing skin, our model can easily be generalized to arbitrary biological structures to explore the physiology and pathology of stretch-induced growth of other living systems such as hearts, arteries, bladders, intestines, ureters, muscles, and nerves.