Combining perturbative-QCD inspired models for multiple jet production with low pr multistring phenomenology, we develop a Monte Carlo event generator HUING to study jet and multiparticle production in high energy pp, pA, and A A collisions. The model includes multiple minijet production, nuclear shadowing of parton distribution functions, and a schematic mechanism of jet interactions in dense matter. Glauber geometry for multiple collisions is used to calculate pA and A A collisions. The phenomenological parameters are adjusted to reproduce essential features of pp multiparticle production data for a wide energy range (&s = 5—2000 GeV). Illustrative tests of the model on p+ A and light-ion B+A data at &s =20 GeV/nucleon and predictions for Au+Au at energies of the BNL Relativistic Heavy Ion Collider (&s =200 GeV/nucleon) are given.