A gear coupling is one of the most difficult couplings to design used in industry , because of the complication for loads distribution between the teeth under misalignment shafts conditions . This paper aims to study the importance of crown to analysis the failure causes of gearcouplings of gas recirculation fans in Banias power station. It presents the stress analysis of mating teeth of gear coupling to find maximum contactstress in its teeth for two situations : crown and straight tooth contact for specialmisalignmentangle. For the analysis,Medium Carbon Steel are used as the material of gear coupling . FEA is done in finite element software ANSYS 14.5. The results obtained from Finite Element Analysis (FEA) are compared with theoretical Hertzian equation values. Both results agree very well. This indicates that the FEM model is accurate . Results show that With straight hub teeth, there is a high concentration of load under misaligned conditions. While Crowned flanks provide optimal load distribution .