Methods of preparing biological tissue for bioprosthetic valves include providing fresh biological tissue; treating the tissue with an aqueous cellulose solution for a time sufficient to allow the fluid in the tissue to be replaced by the aqueous cellulose solution; and cross-linking the tissue, wherein the treating step is performed prior to, during, after, or both prior to and after the cross-linking step. The methods may include storing the cellulose-treated and cross-linked tissue in an aqueous solution; or drying the cellulose-treated and cross-linked tissue by a vacuum-drying or lyophilization process, and storing the dried tissue in a dry, ambient environment. The treated tissue may be in the form of a tissue component for a bioprosthetic valve, a valve assembly for a bioprosthetic valve or a fully assembled bioprosthetic valve incorporating the tissue.