A turbine casing has a front casing segment around a turbine longitudinal axis with first and second front casing part-segments, and a rear casing segment, around the longitudinal axis with first and second rear casing part-segments. The rear casing segment is downstream of the front casing segment in the direction of flow and fastened to the front casing segment via a rear vertical flange of the rear casing segment and a front vertical flange of the front casing segment, forming a cross-shaped joint. A protrusion surrounding the longitudinal axis is formed on the front casing segment in a region of the front vertical flange and extends parallel to the longitudinal axis and protrudes from the front vertical flange in the flow direction. A circumferential seal device is on an outer side, facing away from the longitudinal axis, of the protrusion, and seals the protrusion against the rear casing segment.