The ice shelf caverns around Antarctica are sources of cold and fresh water which contributes to the formation of Antarctic bottom water and thus to the ventilation of the deep basins of the World Ocean. While a realistic simulation of the cavern circulation requires high resolution, because of the complicated bottom topography and ice shelf morphology, the physics of melting and freezing at the ice shelf base is relatively simple. We have developed an analytically solvable box model of the cavern thermohaline state, using the formulation of melting and freezing as in Olbers and Hellmer (2010). There is high resolution along the cavern's path of the overturning circulation whereas the cross-path resolution is fairly coarse. The circulation in the cavern is prescribed and used as a tuning parameter to constrain the solution by attempting to match observed ranges for outflow temperature and salinity at the ice shelf front as well as of the mean basal melt rate. The method, tested for six Antarctic ice shelves, can be used for a quick estimate of melt/freeze rates and the overturning rate in particular caverns, given the temperature and salinity of the inflow and the above mentioned constrains for outflow and melting. In turn, the model can also be used for testing the compatibility of remotely sensed basal mass loss with observed cavern inflow characteristics.