Shear strengthening of reinforced concrete (RC) beams with externally bonded reinforcement (EBR) using carbon fiber reinforced polymer (CFRP) plates and sheets have become a widely accepted practice. To avoid the associated premature debonding failure, this study presents an experimental and analytical investigation on the use of bore-epoxy as an anchorage system for CFRP plates and sheets bonded on both sides of shear deficient RC beams of rectangular cross-sections. Nine (9) RC beams were prepared and strengthened with CFRP plates and sheets as EBR with bore-epoxy anchorage system considering different bore diameters and tested under four point bending. The results indicate that RC beams strengthened with bore-epoxy anchorage system have high shear strength as compared with the unstrengthened control beam and those strenghtended with the conventional EBR approach (without boring). The increase in the shear strength over the control beam was found to be up to 67 % and 121 % for cases of CFRP plates and sheets, respectively. Moreover, the increase of shear strength in comparison with the conventional EBR method ranged from 9.33 % to 20.36 % for CFRP plates and from 12.97 % to 36.10 % for CFRP sheets. Consistently, the contribution of bore-epoxy on the shear strength increased with the increase of bore diameter. Consequently, the existing formulas in the ACI440.2 R for predicting the shear strength of FRP strengthened RC beams were modified to incorporate the improvement made by the proposed bore-epoxy approach. The revised models predicted the experimental shear strength of RC beams, strengthened with bore-epoxy, with a good level of accuracy with average mean absolute percentage error (MAPE) = 6.07 %, 14.71 %, normalized mean square error (NMSE) = 0.097, 0.16, and coefficient of determination R2 = 0.912, 0.974 for plates and sheets, respectively.