Cardiovascular diseases, frequently associated to the formation of aneurisms, are the mayor cause of mortality and morbidity in the world. Due to the increased need for the regeneration of arteries and veins, several natural and synthetic biopolymers such as poly(glycerol sebacate), PGS, have been studied to make blood vessel constructs. PGS elastomeric properties develop after it is crosslinked; however, the poor solubility of the material limits the process to fabricate useful constructs for tissue engineering by electrospinning, casting, or other methods. The structure and properties of electrospun scaffolds made from soluble poly(glycerol sebacate) and poly(ε- caprolactone), are reported here. Soluble PGS oligomers (o-PGS) of different molecular weight, obtained by the polycondensation reaction of sebacic acid and glycerol, were analyzed, including molecular structure, physical properties and solubility. Temperature, reactor atmosphere, and time of reaction strongly influenced the solubility, the molecular weight and molecular structure. To improve o-PGS processing and properties it was mixed with PCL to make electrospun scaffolds. In order to process the mixture by electrospinning, homogeneous solutions o-PGS and PCL were prepared. Because PCL is hydrophobic and o-PGS is hydrophilic selected solvent mixtures were tested to form the homogeneous solutions; the materials dissolved in a mixture of THF:DMF:DCM. Typical electrospinning parameters for preparing the tubular scaffolds at room conditions were: voltage 17.5 kV, needle-collector distance 20 cm and, relative humidity 30-35%, flow injection 0.5 to 2.0 ml/h. The initial mechanical properties of the biodegradable scaffolds were better than those made of natural grafts; the Young’s modulus ranged from 7.6 to 13.0 MPa, depending on electrospinning process parameters. The morphology and physical properties of electrospun PGS/PCL tubular scaffolds show useful features not found in similar constructs made by other methods. The 3D tubular scaffolds were built-up of layered porous walls to produce constructs of different pore size and fibers of different diameter. The porous area was one to two orders of magnitude higher than those produced at micrometer scale by conventional melting and dry/wet spinning methods. These scaffolds show useful characteristics for regenerative medicine such as physical properties; nanometric diameters; high surface/volume ratio; and potentiallity for adhesion and growth of living cells.