A TRV-type turbine casing includes inner and outer annular shrouds that extend one inside the other and about the same axis and are connected together by arms. A tool for disassembling and moving the casing has a lower carriage for moving the tool, and an upper plate to be attached to the turbine casing. The plate is supported by the carriage and includes first members that cooperate with a first annular flange of one of the shrouds to support the casing and axially immobilize the casing relative to the tool. The plate further includes second members that cooperate with a second annular flange of the other shroud in order to prevent and/or guide the rotation of the casing about the axis.