Perturbations from asteroids and Trans-Neptunian Objects (TNOs) produce a significant effect on the orbits of planets and should be taken into account when high-accuracy planetary ephemerides are constructed. On the other hand, from an analysis of motion of the major planets some physical parameters of the asteroids and TNOs may be obtained. The experiment showed that fitting ephemerides from only several of the largest asteroids is insufficient; at present the perturbations from more than 300 asteroids have been taken into account. Methods of estimating asteroid masses are discussed in this paper. Influence of TNOs on the motion of major planets is also considered. Masses of several asteroids that perturb Mars most strongly, the mass and the radius of the asteroid ring, the mass of the TNO ring, as well as the total masses of the main belt asteroids and all TNOs have been estimated while fitting the high-precision numerical ephemerides EPM2008 of IAA RAS to accurate ranging data (1961-2008) of planets and spacecraft orbiting near planets or landing on them.