LUCIAE, a hadronic and string cascade model and its corresponding event generator are used to analyse strangeness production singly and multiply in p-Pb and Pb-Pb collisions at 158 A GeV. Spectra of multiplicity and transverse mass for single (Λ, Λ) and multiple (Ξ-, Ξ-, Ω-, Ω-) strangeness are given. In LUCIAE model it suggests a physical mechanism, i.e. the dependence of the strange quark suppression factor on incident energy, projectile mass and centrality of colliding system might result in increase of yield of strange particles with increasing the above three parameters. Calculations from the model reconstruct well the WA97 experimental data: increase of yield of strange particles with increasing centrality and increase of strangeness enhancement with increasing number of strange quarks, in relativistic nucleus-nucleus collisions.