One of the techniques used in the past decade to determine the shape with a good accuracy and estimate certain physical features (volume, mass, moments of inertia) of asteroids is the polyhedral model method. We rebuild the shape of the asteroid 433 Eros using data from 1998 December observations of the probe Near-Earth-Asteroid-Rendezvous-Shoemaker. In our computations, we use a code that avoids singularities from the line integrals of a homogeneous arbitrary shaped polyhedral source. This code evaluates the gravitational potential function and its first- and second-order derivatives. Taking the rotation of asteroid 433 Eros into consideration, the aim of this work is to analyse the dynamics of numerical simulations of 3D initially equatorial orbits near the body. We find that the minimum radius for direct, equatorial circular orbits that cannot impact with the Eros surface is 36 km and the minimum radius for stable orbits is 31 km despite significant perturbations of its orbit. Moreover, as the orbits suffer less perturbations due to the irregular gravitational potential of Eros in the elliptic case, the most significant result of the analysis is that stable orbits exist at a periapsis radius of 29 km for initial eccentricities ei ≤ 0.2.