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Nanoindentation was used to measure hardness before and after room temperature He ion implantation on sputter-deposited V/Ag multilayers of different layer thickness as well as pure Ag and V. The radiation-induced hardening was found to decrease with decreasing individual layer thickness. No change in hardness after implantation was measured in multilayers with a layer thickness of less than 10nm, which is of the order of the average spacing of He bubbles. The pure V films exhibit significant hardening due to a dense distribution of 0.8nm diameter He bubbles, but in the nanocrystalline pure Ag films bubbles grow to a diameter of approximately 20nm and become ineffective in causing hardening. A model describing layer-thickness-dependent radiation hardening in multilayers was developed by extending the Friedel model to take into account the layer thickness and the He bubble spacing.