An undulator-based positron source is proposed for the future International Linear Collider (ILC): the high-intense electron beam passes through a helical undulator to produce a multi-MeV circularly polarized photon beam before it is directed to the interaction point (IP). The photon beam strikes a thin target to produce electron-positron pairs. A maximum active undulator length of 231 m is expected to be appropriate for the ILC center-of-mass energy range Ecm ≥ 250 GeV. Since the photon produced by the undulator is created with an opening angle, some of these photons will hit the superconducting undulator wall. Therefore, photon masks must be installed along the undulator line to keep the power deposited into the undulator walls due to the synchrotron radiation (primary photons) at an acceptable level (1 W/m). This paper will discuss the power deposited into the undulator walls due to the primary photons and secondary particles. Masks inserted in the undulator line are discussed, assuming ideal and realistic undulator fields. In terms of materials, copper or tungsten are considered in detail.