Claus process is a technology to recover elemental sulfur from H2S contained in the feedstocks, Claus Sulfur Recovery Unit is a chemical type of plant so, it is important to study the parameters that control and affect the main chemical reactions and the side reactions to obtain the maximum production of sulfur and the highest efficiency for the sulfur recovery by using the Aspen HYSYS simulation program V11. Actual data of an acid gas feedstock is obtained from a natural gas plant for this study. The feed acid gas flow rate is 0.616 MMSCFD with an H2S concentration of 50.03 % mole introduced into the Claus Unit. This study demonstrated the optimum temperature inside the thermal reactor at 1077 oC that can be controlled and changed with the inlet temperature (the optimum 240 oC) and/or the air-to-acid gas ratio (the optimum 1.09), this temperature achieves the highest efficiency of 68.11% in the thermal reactor by taking into account H2S-2SO2 parameter equal 0 or little more (0.0004). The effluent gases from the thermal reactor are cooled in a waste heat boiler (WHB) to separate the produced liquid sulfur. After the WHB the remaining gases enter the first catalytic reactor where exothermic equilibrium hydrolysis reactions of COS and CS2 and Claus reaction take place so, the chosen optimum temperature needed to be as low as possible while taking into account that the catalyst activity toward hydrolysis reactions enhanced with high temperature, the optimum temperature is 240.5 oC where COS and CS2 conversion efficiency > 90% (the target in the first catalytic reactor) and sulfur conversion efficiency 69.37%. The produced gases from the first reactor enter the condenser to condense any sulfur vapor produced then to the second catalytic reactor, the lowest optimum working temperature is 195 oC that can apply to achieve maximum sulfur conversion efficacy of 72.91% without sulfur condensation inside the reactor and COS & CS2 conversion efficiency 21.03% and 4.86% respectively.