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The orbits of about 3000 fictitious asteroids, representing a possible distribution of bodies in the early Solar System, were investigated by numerical integration spanning 38,000 years to reproduce the observed distribution of outer belt asteroids. This integration interval allowed for a much larger sample size than previous studies. For additional information on non-escape orbits, the behavior of the estimate of the largest Lyapunov characteristic number was utilized to identify strongly chaotic orbits. The equations of the regularized planar elliptic restricted three body problem were derived to handle close encounters with Jupiter. The semimajor axis distribution for non-escape orbits showed an excess of bodies compared with the observed distribution. This excess is associated with mean motion resonances. When the strongly chaotic orbits are eliminated, the resulting distribution of orbits shows qualitative agreement with the present distribution, reproducing the major groups at the 3:2, 4:3, and 1:1 resonances.