The influence of the density-dependent symmetry energy on the balance energy (E bal ) of directed flow from heavy ion collisions (HICs) at incident energies covered by INDRA and MSU experiments is studied, using the updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, especially adapted to low-energy heavy ion collisions (HICs). Four mass-symmetric reactions with total mass numbers between 192 and 394 are chosen for investigating the influence of the symmetry energy on the system-mass dependence of E bal . The results show that the uncertainty in the density dependence of the symmetry potential causes changes of E bal of the order of several MeV, depending on the type of particle considered. The E bal of neutrons from HICs is particularly sensitive to the density dependence of the symmetry potential energy, while the system-mass dependence of E bal of Z = 1 particles is not. symmetry energy, directed flow, balance energy PACS number(s): 21.65.Ef, 25.70.-z, 25.75.Ld Citation:A key objective in the study of heavy ion collisions (HICs), whether using stable or unstable beams, is to collect information about the nuclear equation of state (EoS). For stable nuclei with large mass numbers, the iso-vector part of the EoS is of importance due to the fact of their neutron number N being considerably larger than their proton number Z. Even for initially isospin-symmetric systems, the isospin effect should be taken into account since isospin diffusion and distillation may occur during the non-equilibrium stages of HICs. Essentially the whole collision is an isospin non-equilibrium process [1,2]. It is also well known and quite obvious that the isospin asymmetric EoS, besides in nuclear physics, is very important for understanding many phenomena in astrophysics as, e.g., the physics of neutron stars. At present, the *Corresponding author (email: liqf@hutc.zj.cn) largest uncertainty in the EoS is believed to come mainly from the density-dependent iso-vector part, the symmetry energy. For the isoscalar part, a soft EoS with incompressibility K around 230 MeV has been extracted through comparisons with data [3,4]. Significant progress in constraining the symmetry energy has been made during the past few years. For recent reviews we refer the reader to refs. [5,6]. Despite these achievements, the density dependence of the symmetry energy, especially at supranormal densities, is still not well determined due to strong model dependences [7][8][9][10].To reduce the model influence and to provide additional constraints, more isospin-related observables will have to be put forward, with the aim of arriving at a more authentic final form of the density-dependent symmetry energy. Besides the sensitive observables being studied up to now by several theoretical groups in this field (Please see the review article [5]