This paper presents the DYON simulations of the plasma burn-through phase at Joint European Torus (JET) with the ITER-like wall. The main purpose of the study is to validate the simulations with the ITER-like wall, made of beryllium. Without impurities, the burn-through process of a pure deuterium plasma is described using DYON simulations, and the criterion for deuterium burn-through is derived analytically. The plasma burn-through with impurities are simulated using wall-sputtering models in the DYON code, which are modified for the ITER-like wall. The wall-sputtering models and the validation against JET data are presented. The impact of the assumed plasma parameters in DYON simulations are discussed by means of parameter scans. As a result, the operation space of prefill gas pressure and toroidal electric field for plasma burn-through in JET is compared to the Townsend avalanche criterion.