The method for preparing a tissue construct for medical purposes uses endothelial progenitor cells (EPC) which have not been passaged multiple times and have a content of EOEC (early outgrowth endothelial progenitor cells) and LOEC (late outgrowth endothelial progenitor cells). These cells and fibroblasts and/or muscle cells, viz. myoblasts, myofibroblasts, smooth muscle cells or the progenitors thereof, are, in the form of living cells, seeded onto a matrix or introduced into a matrix in order to yield the tissue construct following further treatment steps. The matrix is preferably a protein preparation, more particularly a fibrinogen preparation. Both the cells and the fibrinogen preparation can be obtained from a single blood sample from a patient. Apart from the preparation of bypass materials, prosthetic vascular graft, tissue patches, conduits and the like, the EOEC-containing EPC culture or suspension is suitable as means for cell transplantation.