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The investigation of the dynamical evolution of small bodies from the classical part of the Kuiper belt is presented. Analytical studies of the motion of bodies from this part of the Kuipert belt showed the existence of the periodic solution corresponding to Keplerian osculating orbits with small eccentricities. Therefore the process of the migration of these bodies to the inner/outer part of the planetary system requires the influence of additional external forces. Our numerical studies of model circular orbits of bodies from the classical part of the Kuiper belt showed that collisions are one of possible mechanisms for the change of their orbits. New orbits have perihelium/aphelium outside of the Kuiper belt. Depending on the value and direction of an added force a body can migrate to the inner part of the solar system, or to leave the solar system on a hyperbolic orbit.