Future FEL operations in the ELETTRA LINAC require a high quality beam with an ultra short bunch. The knowledge of the short-range wakefields in the backward traveling wave (BTW) accelerating structure is needed to predict the beam quality in term of the single bunch energy spread and emittance. To calculate the effect of the longitudinal and transverse wakefileds we have used the time domain numerical approch with a new implicit scheme for calculation of wake potential of short bunches in long structure [1,2]. The wake potentials of the BTW structure are calculated numerically for very short bunches and analytical approximations for wake functions in short and long ranges are obtained by fitting procedures based on analytical estimations.