Abstract: Disclosed is a method that enables measurement of several thicknesses in a section to be inspected of a hollow container with an axial opening, such as a thin-walled yogurt pot. After having inserted the container through its opening onto a contact support and loaded the container in a predetermined space bordered by a position detection unit, thicknesses are determined by using several mobile support members which are each guided by a set orientation guide. The members are slid into the guide, either up to a first contact defined by a stopper in a calibration configuration without the container, or up to a second contact surface defined by the hollow container in an actual measurement configuration, the movement of these members being automatically controlled by a control unit.