The evolution of the Oort comet cloud between 10,000 and 40,000 AU is simulated using Monte Carlo techniques. In total, over 40 million comets are evolved for a period of 250 million years and 1.5 million comets for 4.5 billion years. Perturbations from both the Galactic tidal field and passing stars are included. The loss cone is filled for semimajor axes ⪆30,000 AU, so that comets at greater distances do not contribute to showers. Over the age of the Solar System the comet cloud beyond ∼20,000 AU loses about half its members. If comets are distributed in density as r-3.5 beyond r = 3000 AU, then the background flux of new comets within 2 AU of the Sun should be ∼0.2 comets/year for a cloud of 10 11 comets beyond 3000 AU, with 2% of the time spent in showers, events where the comet flux is more than five times the background rate. Furthermore, the energy distribution of new comets outside of showers should be strongly peaked at 1/ a = 35 × 10 -6 AU -1.