A central therapeutic goal in many applications of modern Biomedicine is the reconstruction of the diseased arterial sections via robust and viable tissue equivalents. In-host remodelling is an emerging technology that exploits the remodelling ability of the host to regenerate tissue. We develop a general theoretical framework of growth and remodeling of arterial tissue starting from a synthetic, degradable, acellularized graft and we demonstrate the potential of mechanistic models to guide the development and assisting in the design of arterial tissue engineered constructs.