The generalized \( k \)-connectivity \( \kappa_k(G) \) of a graph \( G \) was introduced by Chartrand et al. in 1984. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized \( k \)-edge-connectivity. In this paper, we completely determine the precise values of the generalized \( 3 \)-connectivity and generalized \( 3 \)-edge-connectivity for the Cartesian products of some graph classes.