Large volcanic eruptions can have significant effects on the atmosphere and on climate. Comparing the observed effects against model predictions is also a very valuable test of our scientific understanding of how the atmosphere works. This paper describes a model investigation of a hypothetical eruption, about twice the size of that of Pinatubo in 1991, and is unusual that it focuses on the response in the mesosphere -- the part of the atmosphere in the 50-80km altitude range. The eruption deposits aerosol in the tropics in the 20-25km altitude range, in the lower stratosphere and well below the mesosphere. The effect is felt in the mesosphere through dynamical coupling communicated through small-scale gravity waves, which transport momentum and as a result can drive changes in winds and temperatures. The predictions made in the paper will be helpful in future in interpreting changes in the mesosphere observed following volcanic eruptions.