In this paper, we focus on the assessment of the optimal design of the propulsion system of an energyautonomous Hyperloop capsule supplied by batteries. The novelty in this paper is to propose a sizing method for this specific transportation system, and answer the question whether the energy and power requirements of the Hyperloop propulsion are compatible with available power-electronics and battery technologies. By knowing the weight of a pre-determined payload to be transported along pre-determined trajectories, the proposed sizing method minimizes the total number of battery cells that supply the capsule’s propulsion and maximizes its performance. The constraints embed numerically-tractable and discrete-time models of the main components of the electrical propulsion system and the battery, along with a kinematic model of the capsule. Although the optimization problem is non-convex due to the adopted discrete-time formulation, its constraints exhibit a good numerical tractability. After having determined multiple solutions, we identify the dominant ones by using specific metrics. These solutions identify propulsion systems characterized by energy reservoirs with an energy capacity in the order of 0.5 MWh and a power rating below 6.25 MW, and enable an energy consumption between 10-50 Wh/km/passenger depending on the length of the trajectory.