Electrospinning is an innovative new fibre technology that aims to design and fabricate membranes suitable for a wide range of tissue engineering (TE) applications including vascular grafts, which is the main objective of this research work. This study dealt with fabricating and characterising bilayer structures comprised of an electrospun sheet made of polycaprolactone (PCL, inner layer) and an outer layer made of poly lactic-co-glycolic acid (PLGA) and a coaxial porous scaffold with a micrometre fibre structure was successfully produced. The membranes' propriety for intended biomedical applications was assessed by evaluating their morphological structure/physical properties and structural integrity when they underwent the degradation process. A scanning electron microscope (SEM) was used to assess changes in the electrospun scaffolds' structural morphology such as in their fibre diameter, pore size (μm) and the porosity of the scaffold surface which was measured with Image J software. During the 12-week degradation process at room temperature, most of the scaffolds showed a similar trend in their degradation rate except the 60 min scaffolds. The coaxial scaffold had significantly less mass loss than the bilayer PCL/PLGA scaffold with 1.348% and 18.3%, respectively. The mechanical properties of the fibrous membranes were measured and the coaxial scaffolds showed greater tensile strength and elongation at break (%) compared to the bilayer scaffolds. According to the results obtained in this study, it can be concluded that a scaffold made with a coaxial needle is more suitable for tissue engineering applications due to the improved quality and functionality of the resulting polymeric membrane compared to the basic electrospinning process. However, whilst fabricating a vascular graft is the main aim of this research work, the biological data will not present in this paper.