The present invention relates to a process for directly preparing cell supporting structures by electrospinning, carried out with an installation comprising a square-shaped or an octagonal-shaped collector made of austenitic steel, having on the edges a lattice of slits whereon there is alternately placed, on both faces, a unidirectional or bidirectional arrangement of yarns of absorbable nature representing the matrix. The matrix and the yarns are made of different bioabsorbable polymers ensuring an optimal bioerosion duration and an optimal duration for maintaining the mechanical strength of the resulting membranes. From the thus resulting composite membranes there can be manufactured tubes for 3D tissue growth by bonding on template with the dissolved matrix polymer.
