We have compiled an extensive dataset on potential parts of the Monoceros tidal stream and performed an exhaustive survey of dwarf galaxy semi-analytic orbits in order to constrain its orbital properties . The best-fit orbits are subsequently realized as self-consistent N -body simulations in order to reproduce the spatial and velocity distribution of satellite debris . We find that all kinematic and geometric constraints can be fit by a single stream allowing for multiple wraps . The orbital eccentricity and inclination of the progenitor are strongly constrained to be e = 0.10 \pm 0.05 and i = 25 ^ { \circ } \pm 5 ^ { \circ } . Ten new estimates of proper motions from the Sloan Digital Sky Survey ( SDSS ) clearly exclude all retrograde orbits . Particles lost by the satellite populate two , nearly concentric rings naturally explaining the detection of stream stars at both 6–8 kpc ( Ibata et al . 2003 , Newberg et al . 2003 ) and 12–18 kpc ( the Tri/And stream ; Rocha-Pinto et al . 2003 ) from the Sun . We have attempted to predict the present location of the Monoceros stream progenitor using different information : ( i ) the kinematical and spatial distribution of detections and ( ii ) the different mean metallicity in the innner and the outer rings . Due to the lack of observational data in the whole range of Galactic latitudes , the geometrical/kinematical constraints leads to a wide range of possible locations . By associating older parts of the model stream with lower metallicity parts of the observed data , we argue in favor of a current location of l \sim 245 ,b \sim - 18 . , with a distance to the Sun r _ { s } \simeq 15 kpc . The mass of the progenitor has been poorly constrained due to the slow orbital decay . Similar fits have been obtained for masses ( 3 - 9 ) \times 10 ^ { 8 } M _ { \odot } . We have analyzed to possible common origin of the Canis Major dwarf and the Monoceros stream . Canis Major dwarf moves on a prograde , nearly circular orbit ( e \simeq 0.16 ) in the Milky Way disk ( i \simeq 4 ^ { +14 } _ { -4 } deg . ) . This orbital inclination is too low to account for the large vertical dispersion of stream stars . However , the bimodal distribution of radial velocities in the central region found by Martin et al . ( 2004b ) probably indicates that their selection criteria to indentifying dwarf stars lead to a contamination of background stars . In that case , the kinematical data outlined above might result to an underestimated orbital inclination . Lastly , the distance estimation to Canis Major dwarf is around a factor two smaller than that obtained from our model . Unfortunately , the possible identification of the Monoceros stream progenitor in Canis Major remains unclear .