A twin-shaft vacuum pump includes a pump chamber, a pair of rotary pistons disposed in the pump chamber, and plates which laterally delimit the pump chamber, and a housing ring which peripherally delimits the pump chamber. In order to increase the ability of the pump to withstand thermal stresses, the housing ring and the rotary pistons are made of different materials, with the coefficient of expansion of the piston material being lower than the coefficient of expansion of the housing material. Other improvements include cooling of the lateral end plates, cooling of the rotors, and the provision of sleeves which serve to fix the position of the rotors on the shafts and which are composed of a material whose coefficient of expansion is lower than that of the rotor material.