The Poisson and Vlasov equations are solved self-consistently for realistic Galaxy models which include multiple disk components, a Population II spheroid, and an unseen massive halo. The total amount of matter in the vicinity of the Sun is determined by comparing the observed distributions of tracer stars, samples of F dwarfs and of K giants, with the predictions of the Galaxy models. Results are obtained for a number of different assumed distributions of the unseen disk mass. The major uncertainties, observational and theoretical, are estimated. For all the observed samples, typical models imply that about half of the mass in the solar vicinity must be in the form of unobserved matter. The volume density of unobserved material near the Sun is about 0.1M
−3; the corresponding column density is about 30M
−2. This so far unseen material must be in a disk with an exponential scale height of less than 0.7 kpc. If the unseen material is in the form of stars with masses less than 0.1M
⊙, then the nearest such object is about 1 pc away and has a proper motion of more than 1 arcsecond per year.