A projective plane of order q consists of a set of q 2 + q + 1 points and a set of lines q 2 + q + 1, there are exactly q + 1 points on each line and q + 1 lines pass through each point. A (k, n)-arc is a set of k points, such that there is some n but no n + 1 are collinear, where n ≥ 2 and a (k, n)-arc is complete if there is no (k + 1, n) -arc containing it. In this paper the classification of (k, n) -arcs in 𝑃(2, q) for the projective plane of order eight has been done using different methods.