The gasification apparatus for gasification of finely divided combustible material under pressure includes a gasification reactor which produces a crude gas, a quenching pipe and a convection-heated boiler with a boiler housing, all mounted inside a pressurized vessel. A gas flow guiding device is provided above the quenching pipe for conducting a mixed gas flow containing the crude gas and a quenching gas from the quenching pipe into the convection-heated boiler which surrounds the quenching pipe concentrically. A gas outlet device is provided for the gas flow from the convection-heated boiler and from the pressurized vessel. The gasification reactor is supported at its bottom end in the pressurized vessel at anchoring points. The convection-heated surface elements of the convection-heated boiler are supported by the quenching pipe and the boiler housing but in a stress-free manner. A quenching gas inlet device is provided and includes a circumferential gap between an inlet section of the quenching pipe and an adjacent outlet section of the gasification reactor through which a quenching gas is conducted to form, together with the crude gas, the mixed gas flow.