N-body simulations of the interaction between the Sagittarius dwarf galaxy and the Milky Way are performed to study whether it is possible to reproduce both the bifurcations in the tidal streams and the physical properties of Sagittarius. Both galaxies are simulated as sets of particles (live potentials). The initial structures are formed using GALIC and the gravitational interaction between these galaxies is simulated with gadget-2. Sagittarius initially is simulated as a rotating disk-type galaxy with two components: dark matter halo and stellar disk and the Milky Way is a disk galaxy with three components: dark matter halo, stellar disk and central spheroid. Several angles between the orbital angular momentum and the disc angular momentum in the range 180º ≤ θ ≤ 0º were simulated, showing that, although the position and physical properties of Sagittarius are not reproduced entirely by the remnant, the bifurcations appear clearly when 180º ≤ θ < 90º.