The paper presents a new method for manufacturing hollow shafts, where tubes are used as billet. First, the design of a specially designed forging machine for rotary compression is described. The machine is then numerically tested with regard to its strength, and the effect of elastic strains of the roll system on the quality of produced parts is determined. The machine's strength is calculated by the finite element method using the NX Nastran program. Technological capabilities of the machine are determined, too. Next, the results of the modeling of the rotary compression process for a hollow stepped shafts by the finite element method are given. The process for manufacturing hollow shafts was modeled using the Simufact. Forming simulation program. The FEM results are then verified experimentally in the designed forging machine for rotary compression. The experimental results confirm that axisymmetric hollow shafts can be produced by the rotary compression method. It is also confirmed that numerical methods are suitable for investigating both machine design and metal forming processes.