Measuring apparatus (50) of geometrical parameters of cylinders, rolls and similar elements (11), used for the rolling of flat products operating on a machine for the grinding of said cylinders with an autonomous movement, i.e. with a movement independent of the translation movement of the grinding wheel or other parts, characterized in that it comprises at least four sensors (54, 55), situated on a surface orthogonal to the cylinder (11) or roll and in that at least two of said sensors are situated in opposite positions.