A parametric study has been conducted using the finite element analysis (FEA) technique to investigate the local buckling response of pipelines with axial groove corrosion under combined loads. The developed model used in the analyses has been validated against experimental tests. A large number of parameters such as the diameter to thickness ratio (D/t), axial load ratio (σa/σy), internal pressure ratio (p/py), defect circumferential length ratio (lc/D), defect depth ratio (d/t) and material properties (stress-strain curves) have been evaluated. Utilizing results from the parametric study, non-dimensional equations for predicting the critical local moment (Mlc), critical compressive strain (εlc) and critical local curvature (Фlc) for pipes with internal axial groove corrosion as a ratio to that of plain pipes have been developed through a multi-variable non-linear regression. Good agreement has been achieved between the predicted buckling limits (Mlc/Mlp, εlc/εlp and Фlc/Фlp ratios) using the developed equations and the finite element analyses.