A contact mechanics model is developed to study the mechanical interaction between an elastomeric balloon expander and human skin. Through this interaction, we determine the amount of skin growth and its dependence on the applied load, geometry and elasticity as well as biological factors governing skin growth. For simplicity, we consider rectangular expanders where one of the dimensions is much longer than the other. This simplification allows us to obtain an analytical formulation which is valid for arbitrarily large deformation and contact. In this study, the balloon expander is modeled as an ideal rubber and we used a skin growth model where the growth rate is independent of the elastic stress in the skin. One of the advantages of our formulation is that it can be easily generalized to include more realistic constitutive models for skin growth and elastic behavior of the expander. Our method involves solving algebraic equations and thus is significantly simpler to implement than the commonly used Finite Element method.