A method and apparatus for producing crystals by the Czochralski method whereby the thermal history during crystal growth according to the CZ method can be controlled with ease and accuracy. The apparatus comprises a crucible for receiving a raw material, a heater for heating and melting the raw material, and a heat insulating cylinder disposed so as to surround the crucible and the heater, wherein a portion of the heat insulating cylinder that is located above an upper end of the heater is so configured that its inner diameter is larger than the outer diameter of the heater at its lower end, and that its inner diameter at its upper end is equal to or less than the inner diameter of the heater while its outer diameter is equal to or greater than the outer diameter of the heater. This apparatus is used to produce crystals and to control the temperature distribution inside the crystal producing apparatus or the thermal history of crystals.