The present invention relates to a method of cultivating stem/progenitor cells of the amniotic membrane of umbilical cord that comprises obtaining a tissue explant from the amniotic membrane of umbilical cord and cultivating the tissue explant in suitable cultivation media and cultivation conditions over a suitable period of time. The method may include isolating the stem/progenitor cells from the tissue cultures. The stem cells may be epithelial or mesenchymal stem/progenitor cells. The isolated stem cell cells can have embryonic stem cell-like properties and can be used for various therapeutic purposes.