The present invention provides solutions and methods for preserving living biological materials 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 dihydrogen phosphate, bicarbonate, nitrate, bisulfate and iodide. In one embodiment, preferred for the preservation of platelets, the solutions comprise betaine, sodium chloride and sodium citrate. For the preservation of many living biological materials, the inventive solutions preferably contain a calcium salt selected from the group consisting of calcium sulfate and calcium chloride.