An approximate analytic expression of the eikonal phase for the potential in the form of the symmetrized Fermi function is derived and compared with that obtained by exact calculations. It is shown to be successfully applied to intermediate energy nucleus-nucleus scattering of tens of MeV/nucleon in the framework of a Glauber-Sitenko approach at small angles. In practice, the use of the analytic phase permits one to understand the mechanism of scattering and calculate differential cross sections about two orders faster than with the whole numerical integration.