Abstract: Let G = (V, E) be a graph. A totally irregular total k-labeling f: VUE6{1, 2, ..., k} of a graph G is a total labeling such that for any different vertices x and y of G, their weights wt. (x) and wt. (y) are distinct and for any different edges x1x2 and y1y2 of G, their weights wt. (x1x2) and wt (y1y2) are distinct. The weight wt (x) of a vertex x is the sum of the label of x and the labels of all edges incident with x. The weight wt. (x1x2) of an edge x1x2 is the sum of the label of edge x1 x2 and the labels of vertices x1 and x2. The minimum k for which a graph G has a totally irregular total k-labeling is called the total irregularity strength of G, denoted by ts(G). In this study, we determine the total irregularity strength of M-copy cycles and M-copy paths.