The present invention relates to a method for isolating stem/progenitor cells from the amniotic membrane of umbilical cord, wherein the method comprises separating the amniotic membrane from the other components of the umbilical cord in vitro, culturing the amniotic membrane tissue under conditions allowing cell proliferation, and isolating the stem/progenitor cells from the tissue cultures. The isolated stem cell cells can have embryonic stem cell-like properties and can be used for various therapeutic purposes. In one embodiment, the invention relates to the isolation and cultivation of stem cells such as epithelial and/or mesenchymal stem/progenitor cells under conditions allowing the cells to undergo mitotic expansion. Furthermore, the invention is directed to a method for the differentiation of the isolated stem/progenitor cells into epithelial and/or mesenchymal cells.