  Results for the energy dependence of the elementary kaon production cross
sections in proton-proton collisions are reported. Calculations are performed
within an extended version of the resonance model which was used for the
previous studies of elementary kaon production in pion-nucleon and
pion-$\Delta$ collisions. Although the model treatment is within the {\it
empirical} tree level (observed widths for the resonances are used), it is
fully relativistic, and includes all relevant baryon resonances up to 2 GeV.
One of the purposes of this study is to provide the results for the simulation
codes of subthreshold kaon production in heavy ion collisions. This is the
first, consistent study of the elementary kaon production reactions including
both $\pi B$ and $B B$ ($B=N, \Delta$) collisions on the same footing.
Comparisons are made between the calculated results and the existing
semi-empirical parametrizations which are widely used for the simulation codes,
as well as the experimental data.

Nuclear Theory;High Energy Physics - Phenomenology