Tissue engineered vascular grafts were fabricated using human umbilical vein smooth muscle cells grown onto electrospun gelatine scaffolds. A custom designed electrospinning system was built, with the purpose of fabricating cylindrical scaffolds with circumferentially or diagonally aligned micro-fibres, producing the optimum mechanical properties for use in in-vivo physiological conditions, as well as to direct the cell proliferation and migration, creating circumferentially aligned vascular tissue that mimics a natural vessel’s orientation. The proposed grafts were characterised in terms of their mechanical performance, optimal mass transfer of the limiting nutrient oxygen, as well as cellular performance in static and rotating culture conditions. A mathematical model is proposed in order to predict the mass transfer of oxygen and cellular dynamics in the scaffolds while modelling the scaffold’s changing environment. Most of the physical and biological input parameters required for the mathematical model were determined in experimental studies in this work. A novel fluorescent based, non-invasive, oxygen sensing technique was used to monitor the oxygen concentration in gelatine hydrogels and in liquids, and determine the oxygen diffusion coefficient in gelatine and the oxygen mass transfer coefficient at the gelatine surface, both of which are key parameters of the mathematical model. The mathematical model was successfully validated against experimental data of cell proliferation obtained from the biologically characterised scaffolds and the tissue engineered grafts. The mathematical model was then used to develop the best scaffolds, and optimise the procedure of tissue engineering of vascular grafts using electrospun gelatine fibre scaffolds. This was conducted while taking into consideration the mechanical requirements: graft strength which determines graft functionality; elasticity which determines the conformance with the rest of grafted artery, as well as the suture retention of the graft to assess the ease of surgical implantation. The optimised physical structure and properties of the scaffold, for static and dynamic culture conditions, were linked to the electrospinning parameters used to produce them, delivering a fabrication protocol for the optimum scaffold. Dynamic cell culture conditions for a rotating tubular scaffold resulted in extremely good cell proliferation across the scaffold after 2. 2 days in cell culture, whereas much lower cell proliferation was achieved for the same scaffold after 9 days in static cell culture.