The present invention provides solutions and methods for preserving biological material that enable organs, tissues and cells to be stored for extended periods of time with minimal loss of biological activity. The inventive solutions are substantially isotonic with the biological material to be preserved and are substantially free of univalent oxyanions and of iodide. In one embodiment, the solutions comprise a first neutral solute having a molecular weight of at least about 335 and a solubility in water of at least about 0.3 M, a second neutral solute having a molecular weight of less than about 200 and having both hydrophilic and hydrophobic moieties, and sodium citrate. The inventive solutions preferably contain a calcium salt selected from the group consisting of calcium sulfate and calcium chloride.