The Central Solenoid (CS) is at the core of the EU DEMO tokamak, and has a strong impact on the tokamak design and the overall machine size. By ramping its current, the CS generates a change of magnetic flux, which initiates the plasma, and induces and controls the plasma current. In the context of the conceptual design studies for DEMO coordinated by EUROfusion, the Swiss Plasma Center has developed a simple pre-dimensioning methodology, assuming uniform current density in the solenoid winding pack, and considering the use of Nb3Sn and REBCO. The effects of grading of the superconductor and structural steel are also discussed. Since the CS for the EU DEMO will experience tens of thousands of charge/discharge cycles during its lifetime, mechanical fatigue considerations are taken into account. The proposed methodology has been used for the preliminary design of the CS winding pack, and for a number of parametric analyses in the context of the integrated physics and engineering studies for the EU DEMO machine (identifying the relationship between key performance parameters of the solenoid, such as the generated magnetic flux and the fatigue lifetime).