A pseudo-potential technique has been applied to calculate the annihilation rates for positrons in bubbles of helium gas in gold and silver. The positron pseudo-wavefunction in each case was found to be in a surface state of the metal, the exact form of which displayed a slight dependance on the density of the helium gas. The annihilation rate of the positron was the sum of a nearly constant surface rate and a strongly density dependant annihilation rate with the helium electrons. There is a trend for annihilation with the helium to be greater in metals with low free electron densities, the helium in such metals resting closer to the metal surface thus increasing the overlap of the positron wavefunction with the helium.