The present invention relates to a method for cryopreserving biological material. In particular, the method comprises storing the biological material at a cryopreserving temperature in a composition comprising polyvinyl alcohol (PVA). wherein the composition is substantially free of vitrification-inducing agents such as DMSO and glycerol. The invention also provides methods of inhibiting ice recrystallisation and of reducing cell damage during the warming or thawing of a cryopreserved composition comprising biological material. The invention also relates to processes for producing a biological material, and related kits.