We consider a 3-D model of a dermal wound. The tissue surrounding the wound is slowly healing, and is viewed as an upper convected Maxwell fluid. The velocity satisfies a free boundary problem for a strongly elliptic system with inhomogeneous terms which depend on the fluid pressure P. But P depends on the density of the tissue, which satisfies, together with a number of other variables (densities of cells and signalling molecules) a system of parabolic / hyperbolic equations outside the wound. We shall discuss questions of existence of a solution and properties of the free boundary.