A gas turbine includes a compressor, an annular combustion chamber, and a turbine, a combustion chamber shell of the combustion chamber adjoining the turbine inlet in a transition region in order to introduce the hot gases generated in the combustion chamber into the downstream turbine such that a thermal expansion-induced relative movement between the combustion chamber and the turbine inlet is possible. Combustion chamber shell support elements distributed on the periphery come into contact with a conical contour on the shaft cover due to the thermal expansion that occurs during operation and are supported on said contour. An improvement with respect to loading and service life is achieved in that the conical contour and the machine axis form an angle that allows the combustion chamber shell support elements to slide onto the conical contour.