Radial velocity observations of the F8 V star \upsilon Andromedae taken at Lick and at Whipple Observatories have revealed evidence of three periodicities in the line-of-sight velocity of the star . These periodicities have been interpreted as evidence for at least three low mass companions ( LMCs ) revolving around \upsilon Andromedae . The mass and orbital parameters inferred for these companions raise questions about the dynamical stability of the system . We report here results from our independent analysis of the published radial velocity data as well as new unpublished data taken at Lick Observatory . Our results confirm the finding of three periods in the data . Our best fits to the data , on the assumption that these periods arise from the gravitational perturbations of companions in keplerian orbits , is also generally in agreement , but with some differences , from the earlier findings . We find that the available data do not constrain well the orbital eccentricity of the middle companion in a three-companion model of the data . We also find that in order for our best-fit model to the Lick data to be dynamically stable over the lifetime of the star ( \sim 2 billion years ) , the system must have a mean inclination to the plane of the sky greater than 13 degrees . The corresponding minimum inclination for the best fit to the Whipple data set is 19 degrees . These values imply that the maximum mass for the outer companion can be no greater than about 20 Jupiter masses . Our analysis of the stability of the putative systems also places constraints on the relative inclinations of the orbital planes of the companions . We comment on global versus local ( i.e. , method of steepest descent ) means of finding best-fit orbits from radial velocity data sets .