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.