Abstract: To vitrify a sample, for example a biological sample which has a high water content, without the formation of ice crystals, the sample (10) is placed in a closed test chamber (11) having a chamber outlet (35). The chamber (11), with the sample therein, is filled with a primary fluid without cooling the sample to freezing temperature. This primary fluid may be an alcohol. The sample is vitrified by applying a high-pressure cryogenic fluid against the sample at a substantial pressure. The step of maintaining the pressure is accomplished, in accordance with the invention, by maintaining the outlet (35) from the chamber (11) at least essentially closed by a closing element, typically a valve (41), until the pressure within the sample chamber (11) has reached a predetermined value. The primary fluid may be a portion of the cryogenic fluid itself, for example heated, or even cooled, to an appropriate temperature which, however, will not cause the sample to freeze.