Electron beam (e-beam)-induced changes of surface profile morphology in As c Se 1−c (0.2 < c < 0.5) thin films are investigated as a function of the film composition. It is shown that the extent and value of local surface alterations follow the composition-related changes of glass parameters such as softening temperature and glass network connectivity. The giant e-beam-induced surface relief changes detected in the films As 0.2 Se 0.8 are connected with lateral mass transport, which increases drastically near rigidity transition, i.e. at a coordination number r ∼ 2.2 of the glass structures when the rigidity starts to percolate through the structure. The model of the process, which reflects the compositional dependence of the stimulated mass transport, is presented.