A numerical model of motion for asteroids is developed on the basis of the DE405 theory. The error in position of an asteroid of the main belt is 0.03" for 50-year period of integration. For the computational stability, it is necessary to choose a local truncation error of integration of 10^-14 and to use the double precision of the Standard for Binary Floating-Point Arithmetic IEEE 754-1985. asteroid,dynamical model