Given a graph G = (V, E), a P₂-packing [Pscr ] is a collection of vertex disjoint copies of P₂s in G where a P₂ is a simple path with three vertices and two edges. The MAXIMUM P₂-PACKING problem is to find a P₂-packing [Pscr ] in the input graph G of maximum cardinality. This problem is NP-hard for cubic graphs. In this paper, we give a branch-and-reduce algorithm for the MAXIMUM P₂-PACKING problem in cubic graphs. We analyze the running time of the algorithm using measure-and-conquer and show that it runs in time O^*(1.4366ⁿ) which is faster than previous known exact algorithms where n is the number of vertices in the input graph.