The study of glacial isostatic adjustment (GIA) is gaining an increasingly important role within the geophysical community. Understanding the response of the Earth to loading is crucial in various contexts, ranging from the interpretation of modern satellite geodetic measurements (e.g. GRACE and GOCE) to the projections of future sea level trends in response to climate change. Modern modelling approaches to GIA are based on various techniques that range from purely analytical formulations to fully numerical methods. Despite various teams independently investigating GIA, we do not have a suitably large set of agreed numerical results through which the methods may be validated; a community benchmark data set would clearly be valuable. Following the example of the mantle convection community, here we present, for the first time, the results of a benchmark study of codes designed to model GIA. This has taken place within a collaboration facilitated through European Cooperation in Science and Technology (COST) Action ES0701. The approaches benchmarked are based on significantly different codes and different techniques. The test computations are based on models with spherical symmetry and Maxwell rheology and include inputs from different methods and solution techniques: viscoelastic normal modes, spectral-finite elements and finite elements. The tests involve the loading and tidal Love numbers and their relaxation spectra, the deformation and gravity variations driven by surface loads characterized by simple geometry and time history and the rotational fluctuations in response to glacial unloading. In spite of the significant differences in the numerical methods employed, the test computations show a satisfactory agreement between the results provided by the participants.