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
$$(\Lambda ,\overline \Lambda )$$
and multiple
$$(\Xi ^ - ,\overline {\Xi ^ - } ,\Omega ^ - ,\overline {\Omega ^ - } )$$
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...