A model is presented for calculating the AC losses of a stack of second-generation high temperature superconductor tapes. This model takes as a starting point the model of Clem and co-workers for a stack in which each tape carries the same current. It is based on the assumption that the magnetic flux lines lie parallel to the tapes within the part of the stack where the flux has not penetrated. In this paper we allow for the depth of penetration of field to vary across the stack, and use the Kim model to allow for the variation of Jc with B. The model is applied to the cases of a transport current and an applied field. For a transport current the calculated result differs from the Norris expression for a single tape carrying a uniform current and it does not seem possible to define a suitable average Jc which could be used. Our method also gives a more accurate value for the critical current of the stack than other methods. For an applied field the stack behaves as a solid superconductor with the Jc averaged locally over several tapes, but still allowed to vary throughout the stack on a larger scale. For up to about ten tapes the losses rise rapidly with the number of tapes, but in thicker stacks the tapes shield each other and the losses become that of a slab with a field parallel to the faces.