Observations have revealed a large variety of structures ( global asymmetries , warps , belts , rings ) and dynamical phenomena ( “ falling-evaporating bodies ” or FEBs , the “ \beta Pic dust stream ” ) in the disc of \beta Pictoris , most of which may indicate the presence of one or more planets orbiting the star . Because planets of \beta Pic have not been detected by observations yet , we use dynamical simulations to find “ numerical evidence ” for a planetary system . We show that already one planet at 12 AU with a mass of 2 to 5 M _ { \mathrm { J } } and an eccentricity \la 0.1 can probably account for three major features ( main warp , two inner belts , FEBs ) observed in the \beta Pic disc . The existence of at least two additional planets at about 25 AU and 45 AU from the star seems likely . We find rather strong upper limits of 0.6 M _ { \mathrm { J } } and 0.2 M _ { \mathrm { J } } on the masses of those planets . The same planets could , in principle , also account for the outer rings observed at 500 – 800 AU .