There are two main surgical treatments for vascular diseases, (i) percutaneous stent deployment and (ii) replacement of an atherosclerotic artery with a vascular graft or tissue engineered blood vessel. The aim of this thesis was to develop computational models that could assist in the design of vascular stents and tissue engineered vascular grafts and scaffolds. In this context, finite element (FE) models of stent expansion in idealised and patient specific models of atherosclerotic arteries were developed. Different modelling strategies were investigated and an optimal modelling approach was identified which minimised computational cost without compromising accuracy. Numerical models of thin and thick strut stents were developed using this modelling approach to replicate the ISAR-STEREO clinical trial and the models identified arterial stresses as a suitable measure of stent induced vascular injury. In terms of evaluating vascular graft performance, mechanical characterisation experiments can be conducted in order to develop constitutive models that can be used in FE models of vascular grafts to predict their mechanical behaviour in-situ. In this context, bacterial cellulose (BC), a novel biomaterial, was mechanically characterised and a constitutive model was developed to describe its mechanical response. In addition, the interaction of smooth muscle cells with BC was studied using cell culture experiments. The constitutive model developed for BC was used as an input for a novel multi-scale mechanobiological modelling framework. The mechanobiological model was developed by coupling an FE model of a vascular scaffold and a lattice free agent based model of cell growth dynamics and remodelling in vascular scaffolds. By comparison with published in-vivo and in-vitro works, the model was found to successfully capture the key characteristics of vascular remodelling. It can therefore be used as a predictive tool for the growth and remodelling of vascular scaffolds and grafts