A commercial computer code has been used to simulate the ignition of a flowing ethene-oxygen gas mixture with a hot wire as the ignition source. The reaction kinetics described in this paper have been appended to the program. The reaction scheme consists of two consecutive reactions. The first reaction is of zero order in oxygen and is important at low temperatures. The second reaction has an order larger than zero in oxygen-containing intermediates and dominates in the high-temperature range. The developed model is able to simulate the experimentally observed phenomena quantitatively. We distinguish regions of negligible reaction, local reaction, and explosion. Two criteria determine whether an explosion occurs or not. The first one, the minimum required electrical power supply to the wire, can be predicted very accurately and is a function of the velocity, pressure, and direction of the gas flow-upward or downward. The second criterion is the minimum required oxygen concentration for an explosion. The so-called explosion point is described fairly well as a function of velocity. The influence of the direction of the gas flow is not yet well predicted, because of an incomplete turbulence model. Further experiments are required to prove the adequacy of the model under varying pressure. The dimensionless groups characterizing both criteria are identified.