Near Surface Mounted (NSM) fiber reinforced polymer (FRP) technique with rods/strips attached at the bottom face (B-NSM) has become widely used method for retrofitting concrete structures but has several practical limitations such as accessibility problems and premature debonding. A viable alternative by attaching the NSM FRP reinforcement at the side faces (S-NSM) has recently been presented and showed excellent effectiveness in limited research studies. In this study, a robust finite element (FE) model, featuring state-of-the art modelling techniques and nonlinear properties, is developed to study the flexural behaviour of reinforced concrete (RC) beams strengthened with S-NSM FRP bars. After validating its load, strain, and failure mode predictions with 6 full-size beam experiments, the model was used in an extensive parametric study on 108 new models, evaluating the effects of FRP bar diameter (df), strengthening length (SL), groove elevation (hg), tensile steel reinforcement ratio (ρs), and concrete compressive strength (fc’). In general, the beam ultimate load (Pu) increased with SL, df, ρs, and fc’. The beam ductility also seems to be affected by the studied parameters but in general was satisfactory, averaging 2.30 to 2.73. A regression-based formula was presented for the effective FRP bar length, beyond which the brittle concrete peel-off failure is prevented, and Pu becomes constant. A sectional analysis was also performed coupled with regression, resulting in the development of a simple equation to calculate the FRP strain at beam failure and consequently an improved analytical model for predicting Pu.