A leading-edge model due to McClung is used to describe the run-up and run-out of avalanches. The modeling process results in a singular initial value problem which is solved numerically using an appropriately adapted version of the IDeC method. In Section 1 the model and its parameters are specified. In Section 2 existence, uniqueness and smoothness properties of the analytical solution of the problem are discussed. In Sections 3 and 4 we describe the algorithm and technical details of the implementation. The results of some numerical experiments are given in Section 5.