Results of the collimation studies for the ILC positron source beam line are presented. The calculations of primary positron beam loss are done using the ELEGANT code. The secondary positron and electron beam loss, the synchrotron radiation along the beam line and the bremsstrahlung radiation in the collimators are simulated using the STRUCT code. The first part of the collimation system, located right after the positron source target (0.125 GeV), is used for protection of the RF Linac sections from heating and radiation. The second part of the system is used for final collimation before the beam injection into the Damping Ring at 5 GeV. The calculated power loss in the collimation region is within 100 W/m, with the loss in the collimators of 0.2-5 kW. The beam transfer efficiency from the target to the Damping Ring is 13.5%.