  The increase of effective string tension as a result of the hard gluon kinks
on a string is investigated using a parametrization form. In this form the
effective string tension increasing with energies in hadron-hadron collisions
is due to the mini-jet (gluon) production in the collisions. The data of the
energy dependence of the strange quark suppression factor in hh collisions are
very well reproduced with this mechanism. Meanwhile, the experimental phenomena
of approximate energy independence of the strange quark suppression factor in
e$^+$e$^-$-annihilations are discussed.
