herein described is a method and apparatus for controlling braking and stopping of the slewing of an upper slewing body which is slewingably provided on a construction and hoists a load , represented by a rotary crane , wherein the braking torque for braking the upper slewing body and the braking torque for braking a hoisting load are separately obtained by the calculated slewing angular acceleration , and the whole braking torque is calculated on the basis of both the braking torques , thereby achieving a high accurate control of the slewing stop .