Artin relations in the mapping class group

For every integer a parts per thousand yen 2, we find elements and in the mapping class group of an appropriate orientable surface , satisfying the Artin relation of length . That is, ... = ..., where each side of the equality contains terms. By direct computations, we first find elements and in Mod(S) satisfying Artin relations of every even length a parts per thousand yen 8, and every odd length a parts per thousand yen 3. Then using the theory of Artin groups, we give two more alternative ways for finding Artin relations in Mod(S). The first provides Artin relations of every length a parts per thousand yen 3, while the second produces Artin relations of every even length a parts per thousand yen 6.