This work presents a comprehensive study of the cloak for bending waves theoretically proposed by Farhat et al. [see Phys. Rev. Lett. 103, 024301 (2009)] and later on experimentally realized by Stenger et al. [see Phys. Rev. Lett. 108, 014301 (2012)]. This study uses a semi-analytical approach, the multilayer scattering method, which is based in the Kirchoff-Love wave equation for flexural waves in thin plates. Our approach was unable to reproduce the predicted behavior of the theoretically proposed cloak. This disagreement is here explained in terms of the simplified wave equation employed in the cloak design, which employed unusual boundary conditions for the cloaking shell. However, our approach reproduces fairly well the measured displacement maps for the fabricated cloak, indicating the validity of our approach. Also, the cloak quality has been here analyzed using the so called averaged visibility and the scattering cross section. The results obtained from both analysis let us to conclude that there is room for further improvements of this type of flexural wave cloak by using better design procedures.