Apparatus are provided for preventing the formation of ice crystals in a biological sample containing a non-Newtonian fluid as a cryopreservation medium. The apparatus may be used to prevent ice formation during cryopreservation of biological samples, or during warming of cryopreserved biological samples, by changing the viscosity of the non-Newtonian fluid. The apparatus (200) comprises a housing (202) for a container (212) containing the biological sample (214) and the non-Newtonian fluid, and a device (204) for inducing a change in viscosity of the cryopreservation medium. The change in viscosity may be increased by inducing shear thickening of the cryopreservation medium, or the change in viscosity may be decreased by inducing shear thinning of the cryopreservation medium. Possible viscosity-changing devices comprise a tapping device, a piston, a rotating device, a compression device, a sound generating device, a permanent magnet or a electromagnetic field generating device. The apparatus may further include a temperature control device.