This paper presents the results of research on improving the efficiency of the mechanical agglomeration through describing the influence of the shape of the piston pressure face on the limit force value. The focus of this study is the geometrical parameters which are describing the shape of the piston pressure face. Where these parameters influence on the value of the limit stress in the process of mechanical agglomeration of crystallized carbon dioxide. The first part of the paper proposes a model describing the influence of the geometric parameters of the piston pressure face on the value of axial force during the subsequent compression phase of the process. The research part of the paper presents the empirical research results to verify the proposed model. The results of the work will be used to determine the influence of the described geometrical parameters of the dry ice residue on the axial force value. The derived mathematical model will be used for defining the design requirements as the starting point for the design and building of dry ice compression and granulation machines.