In this paper, we study optimality conditions of quasi approximate solutions for nonsmooth semi-infinite programming problems (for short, (SIP)), in terms of ε-upper semi-regular semi-convexificator which is introduced here. Some classes of functions, namely (ε − ∂ * ε)-pseudoconvex functions and (ε − ∂ * ε)-quasiconvex functions with respect to a given ε-upper semi-regular semi-convexificator are introduced, respectively. By utilizing these new concepts, sufficient optimality conditions of approximate solutions for the nonsmooth (SIP) are established. Moreover, as an application, optimality conditions of quasi approximate weakly efficient solution for nonsmooth multi-objective semi-infinite programming problems (for short, (MOSIP)) are presented.