The Medium Energy Beam Transport (MEBT) section of the ESS Linear Accelerator (linac) will be composed of several magnetic quadrupoles, re-bunching cavities, beam choppers, beam dumps and a diagnostic bench. After the beam is accelerated up to 3 MeV in the Radio Frequency Quadrupole (RFQ) cavity, the longitudinal and transversal bunches of particles are slightly broadened. The main task of the re-bunching cavities in the MEBT is to maintain the longitudinal focusing and to match the beam from the RFQ into the MEBT and from the MEBT into the Drift Tube Linac (DTL). This report summarizes the work done on the ElectroMagnetic (EM) design of the re-bunching cavities. The EM design is not independent of other design issues (tuning scheme, mechanical design, ...), so although there will be specific technical reports on these subjects, some aspects will be discussed also in this document.