For a graph G we define a k-labeling ρ such that the edges of G are labeled with integers {1, 2,..., ke} and the vertices of G are labeled with even integers {0, 2,..., 2kv}, where k= max {ke, 2kv}. The labeling ρ is called an edge irregular reflexive k-labeling if distinct edges have distinct weights, where the edge weight is defined as the sum of the label of that edge and the labels of its ends. The smallest k for which such a labeling exists is called the reflexive edge strength of G. In this paper we give exact values for the reflexive edge strength for prisms, wheels, baskets and fans.