The behaviour and activity of the genioglossus muscle during sleep is of considerable interest to investigators of obstructive sleep apnea syndrome. Therefore, we contribute an model of genioglossus EMG activity during breathing, based on recent physiological findings. We present the modelling techniques and simulation results. The model incorporates new data on fibre type, motor unit type and motor unit firing characteristics. Although we report its use for modelling genioglossus surface EMG, this model can be used to simulate both genioglossus surface and intramuscular EMGs of various electrode configurations. We also discuss the simulation results in the context of the limited experimental data available for surface genioglossus EMG in obstructive sleep apnea.