Abstract: The elevator car contains an elevator car body substantially horizontally supported at low friction at a support frame. The elevator car body is supported at a bottom yoke of the support frame by, for example, three hydraulic suspension units and is maintained in floating position during travel of the elevator car. During such travel, only the support frame carries out substantially horizontally directed thrust movements or vibrations which are generated by the associated guide rails, whereas the elevator car body remains in position or at rest due to its mass inertia and the low friction support. The floating elevator car body can be displaced into predeterminate positions by means of actuating cylinders. During travel of the elevator car, the floating elevator car body is displaced into a position spaced at a greater distance from the elevator shaft wall on the side of the elevator door for increasing the movement clearance.