Digestion vessels with PTFE liners designed specifically for the microwave. A high-strength, transparent, microwaveable material surrounds the chemically inert PTFE liners, allowing these vessels to be placed directly in a microwave oven for specific, rapid heating. The high temperatures and pressures developing in the vessels as a result of this special procedure result in an extremely aggressive digestion process, without overheating the outer sheath. With form-fitting seals and integrated overpressure protection. Special ovens are not required; the vessels can be used in any lab or household microwave.