Summary: Since the turn of the century there have been several notions of convergence for subsets of metric spaces appear in the literature. One of these notions is the concept of epi-convergence. In this paper we present definitions of epi-Cesàro convergence for sequences of lower semicontinuous functions from \(X\) to \([-\infty,\infty]\) and Kuratowski Cesàro convergence of sequences of sets. Also we characterize the connection between epi-Cesàro convergence of sequences of functions and Kuratowski Cesàro convergence of their epigraphs.