The paper presents a new process for flanging hollow parts. This process is performed using a specially designed set of tools with movable sleeves. The principle of operation of the tool set is described and examples of the numerical analysis results are given. The FEM simulation was performed on the assumption that the hot-formed hollow workpiece (tube) is made of AlMgSi aluminum alloy. The obtained FEM results show changes in the workpiece shape during flanging, variations in the forming force and the damage function distribution computed according to the C-L failure criterion. The theoretical results of the new flanging method provided basis for experimental tests.