Using a hadron-string cascade model LUCIAE, the phi -meson production in nuclear collisions (p + Pb and Pb + Pb) and elementary collisions p + p were studied systematically. Within the framework of the model, the experimentally measured phi enhancement in p + Ph and Pb + Pb over p + p collisions can be mostly explained by the collective effects in the gluon string emission and the reduction of the s-quark suppre...