Theoretical analysis results of the effect of out-of-contact deformation of a tube wall on the input and the output of a cone die on stresses of the plastic pressing process depending on deformation conditions are presented. A degree of processed metal, geometric parameters of tools and a tubular billet were taken into account. Diagrams of axial stress changing depending on different parameters were plotted. The theoretical and experimental data is matched well and can be used for design of processes of tube reduction.