The formalism for a Monte Carlo computer program which simulates slowing down and scattering of energetic ions in amorphous targets is presented. It was developed for determining ion range and damage distributions as well as angular and energy distributions of backscattered and transmitted ions. The computer program provides particularly high computer efficiency, while still maintaining a high degree of accuracy. This is achieved mainly by applying a new analytic formula for determining nuclear scattering angles based on the Molière potential, and by suitably expanding the distance between collisions at high energies. With these improvements it becomes feasible for the first time to assess accurately both low and high energy problems with high precision using a single simulation program.