A model for calculating the morphological relaxation of two-dimensional glass profiles for arbitrary temperature-time schedules is described. The model is based on a Fourier expansion of the surface profile for which the decay with time can easily be calculated for each of the separate terms. The effect of the variable temperature with time was accounted for by discretization of the temperature-time profile. Necessary input data are the viscosity and surface tension of the glass. The sensitivity to various geometrical details is limited, but heating/cooling effects appeared to be important. The predictions of the model are verified by measurements on glass samples with various profiles and relaxed according to a certain temperature-time schedule. Using a surface tension value of 0.19 N m(-1), as determined with recent fibre-on-plate experiments, excellent agreement between theory and experiment was obtained. Possible options for extension to three-dimensional profiles are indicated.