The centrifugal disc finishing process is an abrasive technique of mass machining, and it is very effective but very frequently time consuming. In this paper, a simulation of the centrifugal disc finishing process was presented in order to estimate the kinetic energy distribution of the working medium and to find its regions that make the process more efficient. Numerical results were obtained using an explicit method in the Ansys/Ls-Dyna program. Due to the fact that the physical properties of numerous objects in free motion need to be calculated in a simulation process, the discrete element method (DEM) was used. Results from the numerical simulations indicate that the velocity and energy of particles is variable in an axial cross-section of working medium. The article presents particle velocity distributions in the working chamber for various rotational speeds of the rotor. The typical changes in velocity in the function of time are also discussed. Statistical important functions of the average kinetic energy of the working medium and accumulated energy by machining surface have been estimated in respect to the rotational speed and machining time with a high value of adjustment coefficients. This article constitutes the first stage of research, which is continued in order to experimentally verify the results in the real process, as presented in the companion paper (Part 2: Experimental analysis with the use of acoustic emission signal).