LUCIAE, a hadronic and string cascade model and its corresponding event gen
erator are used to analyse strangeness production singly and multiply in p-
Pb and Pb-Pb collisions at 158 A GeV. Spectra of multiplicity and transvers
e mass for single (Lambda, <(Lambda)over bar>) and multiple (Xi(-), <(Xi(-)
)over bar>, Omega(-), <(Omega(-))over bar>) strangeness are given. In LUCIA
E model it suggests a physical mechanism, i.e. the dependence of the strang
e quark suppression factor on incident energy, projectile mass and centrali
ty of colliding system might result in increase of yield of strange particl
es with increasing the above three parameters. Calculations from the model
reconstruct well the WA97 experimental data: increase of yield of strange p
articles with increasing centrality and increase of strangeness enhancement
with increasing number of strange quarks, in relativistic nucleus-nucleus
collisions.