Cellulose acetate (CA) thin, porous membranes were produced by electrospinning precursor polymer solutions in acetone at room temperature. During this process, CA nanofibers were produced when a high electric field of 12 kV was applied to the precursor solution. The diameters of fibers obtained varied from 100 nm to 1.2 μm while the average diameter was approximately 500 nm. The electrospinning parameters used to control the morphology of the fibers and their membranes are flow rate, the distance between the syringe needle that ejects fluid and the collector, and the voltage applied. These membranes were used as scaffolds for microvascular cells growth. The structure of the membranes that were produced mimic the topography and porosity of extracellular matrix (ECM) in two key ways. The fiber diameter mimics extracellular protein fiber diameter, thus enabling cellular attachment and facilitating cellular migration. The porosity mimics that of extracellular matrix such that microvascular capillary tube formation is enhanced. The non-woven fiber mats were examined by means of electron microscopy and the nanofibers were seen to be oriented randomly. The issue of strengthening the CA scaffold is currently studied by adding ceramic nano-structured component (carbon nanotubes) in the polymer membranes.