The paper presents a preliminary study on a virtual 2-stroke 3-cylinder 0.9 L DI SI supercharged engine running on Hydrogen (H2), able to meet both high performance targets and ultra-low emissions limits (NOx<20 ppm). Combustion is similar to a conventional 4-stroke H2 DI engine, while the design of the cylinder and the actuation law of both intake and exhaust valves are specifically optimized for the 2-stroke cycle. In comparison to a more conventional 2-stroke loop scavenged engine, with piston-controlled ports, the use of poppet valves enables a more flexible control of the gas exchange process and to maintain the same design of a 4-stroke engine for pistons, cylinders block, crankcase and lubrication system. On the other hand, it is more difficult to avoid the short-circuit of the fresh charge, while permeability of the valves becomes quite critical at high engine speed. Therefore, particular care was devoted to the optimization of the intake and exhaust ports geometry, as well as to the valves actuation law. While the development of the scavenging system was mainly supported by CFD-3D simulation, the optimization of the supercharging system is driven by 1D analyses (by GT-Power). Three different supercharging configurations have been analyzed, with different levels of complexity, performance and cost: compact mechanical supercharger, controlled by a by-pass valve; variable geometry turbocharger, assisted by a mechanical supercharger and controlled by a by-pass valve; variable geometry turbocharger, assisted by an electric supercharger. The 1D engine model of the 2-stroke engine is derived as closely as possible from the experimentally calibrated model of a 4-stroke H2 prototype. In particular, the virtual engines share the setup of the predictive combustion and emissions models.