Chronic wound healing is a staggering public health problem, affecting 6.5 million individuals annually in the U.S. Ischemia, caused primarily by peripheral artery diseases, represents a major complicating factor in the healing process. In this talk, I will present a mathematical model of chronic wounds that represents the wounded tissue as a quasi-stationary Maxwell material, and incorporates the major biological processes involved in the wound closure. The model was formulated in terms of a system of partial differential equations with the surface of the open wound as a free boundary. Simulations of the model demonstrate how oxygen deficiency caused by ischemia limit macrophage recruitment to the wound-site and impair wound closure. The results are in tight agreement with recent experimental findings in a porcine model. I will also show analytical results of the model on the large-time asymptotic behavior of the free boundary under different ischemic conditions of the wound.