In this study, a mathematical model of a semi-automatic hand-held weapon is presented. The dynamical equations of motion are derived by utilizing the formalism of Lagrange equations of the second kind. The model is applied to describe motion of P-64 semi-automatic pistol. The characteristics of rheological elements accounting for the mechanical reaction of the human hand are identified and are further used to determine the force and torque which act on the human hand during a shot. Some exemplary results of the conducted parametric study are presented in order to illustrate sensitivity of the system.