WE DESCRIBE THE MATHEMATICAL METHODS AND THE RESULTS OF COMPUTER CALCULATIONS THAT MAKE POSSIBLE THE CHOICE OF THE OPTIMAL PARAMETERS OF A SYSTEM FOR SHAPING A PROTON BEAM OF MICRON SIZE, DEPENDING ON THE REQUIREMENTS IMPOSED ON THE BEAM AND ON THE SYSTEM. THE SHAPING SYSTEM CONSISTS OF TWO DIAPHRAGMS AND FOUR QUADRUPOLE LENSES THAT MAKE UP AN ANTISYMMETRICAL SYSTEM SIMILAR IN ITS PROPERTIES TO AN AXISYMMETRIC LENS.