The Leksell Gamma Knife radiation is collimated both by a fixed primary collimator system and a secondary replaceable collimator. The purpose of this diploma work was to study the dependence of the paediatric patient peripheral doses on the choice of the secondary collimator and for simple radiosurgery treatment plan verify whether the results obtained can be used to estimate peripheral doses if all four secondary collimators are used for gamma knife treatment. An anthropomorphic phantom representing a 10 year old child was used for measurements. Radiophotoluminescent dosimeters placed in the organs of the phantom were used for dose measurements. Secondary collimators are characterized with the diameter of their holes and output factor defined by the vendor. For each of the four secondary collimators, a treatment plan for the same target volume was made and for each collimator the peripheral doses were measured and organ doses were calculated. The highest peripheral doses were measured for a 18 mm collimator. By selecting collimators with smaller apertures (14 mm and 8 mm) the peripheral doses were decreased, which was explained by the smaller radiation leakage. The trend of reducing peripheral doses with the decrease of aperture size was not obtained for the 4 mm collimator. For the 4 mm collimator the average peripheral organ dose was comparable with value obtained for 18 mm collimator and that was explained with much smaller output factor (and the larger irradiation time for the same target dose) for the 4 mm collimator in comparison with other collimators. For each of the organs, a factor representing the ratio of the organ dose and the maximum target dose was calculated. Using these factors for a treatment plan that uses four collimators, the peripheral organ doses were calculated and compared to measured values. The comparison of measured and calculated doses was satisfactory.