This paper presents results for some vertex stress related parameters in respect of specific subfamilies of Kneser graphs. Kneser graphs for which diam(KG(n, k)) = 2 and k ≥ 2 are considered. The note establishes the foundation for researching similar results for Kneser graphs for which diam(KG(n, k)) ≥ 3. In addition some important vertex stress related properties are stated. Finally some results for specific bipartite Kneser graphs i.e. BK(n, 1), n ≥ 3 will be presented. In the conclusion some worthy research avenues are proposed.