An apparatus and method are provided for reducing the drag caused by a complex-section part in an airflow, for example the landing gear of an aircraft, making it possible to optimize the lift/drag ratio and to reduce the aerodynamic noise by reducing the local noise source. To do so, the complex-section part is masked with a special casing. More specifically, the aero-acoustically optimized complex-section metal mechanical part is fitted with an aerodynamically shaped cover made of several longitudinal parts articulated with hinges to facilitate their installation. This cover is attached to at least two supports placed away from one another along the axis of the part, each support locally mating with the section of the part.