This paper presents the results of a numerical investigation into tube flanging by extrusion with a moving sleeve. Two cases of the extrusion process are investigated, each described with a different tool kinematics. Effects of flange diameter, gap height and tool motion on the extrusion process are examined. The numerical analysis is performed on 42CrMo4 steel tubes deformed at ambient temperature. Obtained numerical results are then used to determine metal flow patterns and examine force parameters in the extrusion process, as well as to determine a technological window for the investigated method.