An extension of the intranuclear cascade model is described. The primary hadrons may be pions, kaons, nucleons, and their antiparticles. Secondary particles produced include hyperons or anti-hyperons. A large amount of experimental data is described by the model. The model is constructed via the Monte Carlo generation of complete events, based on a model of the nucleus structure and the hadron/nucleon interaction inside the nucleus. Calculated average multiplicities and single and double differential cross sections are compared with experimental data.