ABSTRACT Common envelope evolution (CEE) is believed to be an important stage in the evolution of binary/multiple stellar systems. Following this stage, the CE is thought to be ejected, leaving behind a compact binary (or a merger product). Although extensively studied, the CEE process is still little understood, and although most binaries have non-negligible eccentricity, the effect of initial eccentricity on the CEE has been little explored. Moreover, most studies assume a complete circularization of the orbit by the CE onset, while observationally such eccentricities are detected in many post-CE binaries. Here we use smoothed particle hydro-dynamical simulations to study the evolution of initially eccentric (0 ≤ e ≤ 0.95) CE-systems. We find that initially eccentric binaries only partially circularize. In addition, higher initial eccentricity leads to a higher eccentricity following the end of the inspiral phase, with eccentricities as high as 0.18 in the most eccentric cases, and even higher if the initial pericentre of the orbit is located inside the star (e.g. following a kick into an eccentric orbit, rather than a smooth transition). CEE of more eccentric binaries leads to enhanced dynamical mass-loss of the CE compared with more circular binaries, and depends on the initial closest approach of the binary. We show that our results and the observed eccentricities of post-CE binaries suggest that the typical assumptions of circular orbits following CEE might potentially be revised. We expect post-CE eccentricities to affect the delay time distributions of various transients such as supernovae, gamma-ray bursts, and gravitational-wave sources by up to tens of per cents.