We propose an ultra-thin elastic cloak to control the scattering of bending waves in isotropic heterogeneous thin plates. The cloak design makes use of the scattering cancellation technique applied, for the first time, to the biharmonic operator describing the propagation of bending waves in thin plates. We first analyze scattering from hard and soft cylindrical objects in the quasistatic limit, then we prove that the scattering of bending waves from an object in the near and far-field regions can be suppressed significantly by covering it with a suitably designed coating. Beyond camouflaging, these findings may have potential applications in protection of buildings from earthquakes and isolating structures from vibrations in the motor vehicle industry.