The multiplicity-free subgroups (strong Gelfand subgroups) of wreath products are investigated. Various useful reduction arguments are presented. In particular, for any finite group G and its normal subgroup K, if G/K is isomorphic to a cyclic group and its order is a multiplicity free integer, then (G,K) is a strong Gelfand pair. Furthermore, we classify all multiplicity-free subgroups of Z/p wreath S_n when n>6. Along the way, we derive various decomposition formulas from some special subgroups of Z/p wreath S_n when n>6.
