The invention discloses a flexible supporting device which is used for solving the technical problem that as an existing supporting device is low in positioning accuracy, the part
machining accuracy is low. According to the technical scheme, the flexible supporting device comprises a left iron core, a left
magnet exciting coil, a left wedge-shaped guide container wall, a left supporting plate, a left wedge-shaped block, a right supporting plate, a right wedge-shaped block, a right wedge-shaped guide container wall, a right
magnet exciting coil, a right iron core and
magnetorheological fluid, and further comprises a
machine frame, a left primary positioning device, a right primary positioning device, a displacement sensor, a supporting rod and a
direct current voltage stabilizing power source; blades are fixed to the left primary positioning device and the right primary positioning device through a bolt, and the left primary positioning device and the right primary positioning device are fixed to the container walls parallel to the direction of a
magnetic field through bolts. The blades are immersed in the
magnetorheological fluid, receding deformation, caused by insufficient rigidity of the blades, of the blades in the
cutting process is avoided, the positioning accuracy of a complex
thin wall part is improved, the rigidity of the complex
thin wall part is accordingly improved, and the high-speed and efficient
machining accuracy and the
machining quality of the complex
thin wall part are guaranteed.