A set of elements of a group is said to generate (or to be the generators of) if the (possibly repeated) application of the generators on themselves and each other is capable of producing all the elements in the group. Given a set of generators (which are obtained by using the built-in Mathematica 8 function GroupGenerators) of , the Cayley graph associated with is defined as the directed connected graph having one vertex associated with each group element and directed edges whenever is a generator. In this Demonstration we construct the Cayley graphs of several types of groups using the CayleyGraph function.