Title An algorithmic analysis of the intersection property Authors P. Jacobs and D. Leemans Reference LMS J. Comput. Math. 7(2004), 284-299. Abstract We give efficient algorithms to test the intersection property and some of its variations on flag-transitive coset geometries. We apply these algorithms to geometries of some sporadic groups, namely the Mathieu groups M_11, M_12, M_22 and M_23, the Janko groups J_1, J_2 and J_3 and the Higman-Sims group HS.