Microscopic radiation damage in a Lennard-Jones amorphous solid is investigated by computer simulations of collision cascades. Molecular-dynamics simulations with various primary knock-on atom (PKA) energies and directions are carried out. Energy outflow from the computational box is accounted for but electronic losses are neglected. The simulations show the PKA energy to spread rapidly among the nearby atoms, and the atomic trajectories disclose such features as replacement collision sequences and focused chains. Vacancies are created in the central region of the cascade and are surrounded by a cloud of interstitials. The defects mainly disappear independently of each other, the vacancies faster than the interstitials. Recombination plays a minor role. At the end of a simulation all the defects created have vanished and little change in the sample volume or structure is observed. The threshold energy for a permanent displacement is found for various PKA directions. The validity of the modified Kinchin-Pease model for an amorphous solid is discussed.