The paper addresses a fundamental problem of tightness of ultra-high vacuum systems (UHV) at cryogenic temperatures in the light of continuum damage mechanics (CDM). The problem of indentation of a rigid punch into an elastic-plastic half-space is investigated based on rate independent plasticity with mixed kinematic and isotropic hardening. The micro-damage fields are modeled by using an anisotropic approach with a kinetic law of damage evolution suitable for ductile materials and cryogenic temperatures. The model has been experimentally validated and the results are used to predict the onset of macro-cracking (loss of tightness) and the corresponding load (contact pressure). The algorithm is applied in the design of UHV systems for particle accelerators. (C) 2009 Published by Elsevier Ltd.