A mathematical model is presented, allowing computer simulations of the system shooter – recoil damper – firearm at an early stage of its motion, when no conscious reactions to input forces occur on the shooter's side. Exemplary computation results are given for a shooter of a mass of 78 kg and a height of 185 cm, firing an M16 rifle or a 12/70 smoothbore hunting weapon, single shot mode. Those results point out the significance of the shooter's training, especially the delay time resulting from conscious response to forcing stimuli, and the benefits accruing from using a damper filled with magnetorheological fluid having time-variable damping characteristics.