One possible method for strengthening deteriorated concrete structures is to externally bond composite material plates to the concrete. To implement such a rehabilitation, the nature of the bond between the composite plate and the concrete must be understood. A single-lap shear test specimen was used to study the bond strength and force transfer of graphite/epoxy composite material plates adhered to concrete. Using a test specimen having a constant bond length, the influence of the surface preparation of the concrete, adhesive type, and concrete strength on the overall bond strength was examined. To determine the characteristics of force transfer from the plate into the concrete, additional bond tests were conducted. Based on the test results, recommendations for obtaining the highest strength bond are made. In addition, conclusions regarding the rate of force transfer and the maximum effective bond length for the joint studied are presented.