Vapour explosions, also called thermal detonations, occur when a liquified gas comes into contact with water. During the contact of the two liquids with considerably different temperatures, intensive boiling of one of them takes place which is accompanied by an explosive increase in pressure. A similar phenomenon also arises in the cooling systems of nuclear-power stations, when, as a result of some accident, the heated particles of the nuclear fuel settle in the cold water. This leads to the explosive boiling of the liquid and to a rapid increase of the pressure. This paper presents analytical and numerical modelling of the behaviour of small-scale single drops of liquified gas in water.