Abstractpresuppositions, theoretical basis, results and general experiences of numrtricsl model calculations of quasi-stationary cathodic spots in (vacuum) arcs are summanzed. The results (mainly related to copper cathodes) comprise the essential physical quantities of the cathode Spot surbrv and (partially) of the cathode spot plasma, i.e. possible states of existence within the Space of pilr:\nicters. Especially, the dependence of these results on changes of the parameters and equations is invcstigatcd. Several examples are presented and interpreted. In any case, the surface roughness of the C:\thcdc is taken into account. Finally, the limitations of the model are discussed, and the great importance of non-stationary (e.g. explosive) processes within the arc spot is emphasized, though such P~~L W S C S arc beyond the scope of this model. The paper is published in two parts. This first part comprises an introduction to scveral aspects of arc spot modeling, the discussion of the physical processes in cathode arc spots and the development of relevant equations to be used in the model.