Abstract : There is growing demand from the industrial and research communities for high gradient, compact RF accelerating structures. The Thomx high gradient structure (HGS) is travelling wave (TW), quasi constant gradient section and will operate at 2998.55 MHz (30°C in vacuum) in the 2π/3 mode. The optimization of the cell shape (Electromagnetic design) has been carried out with the codes HFSS and CST MWS, in order to improve the main RF characteristics of the cavity such as shunt impedance, accelerating gradient, group velocity, modified Poynting vector, surface fields, etc. Prototypes with a reduced number of cells have been designed. For an input power of about 20 MW, EM simulation results show that an average accelerating gradient of 28 MV/m is achieved which corresponds to a peak accelerating gradient of 35 MV/m, a peak surface gradient of 44 MV/m and peak modified Poynting vector S_{cmax} of 0.24 MW/mm².