The modified Claus process is one of the most common technologies for sulfur recovery from acid gas streams. Important design criteria for the Claus unit, when part of an Integrated Gasification Combined Cycle (IGCC) power plant, are the ability to destroy ammonia completely and the ability to recover sulfur thoroughly from a relatively low purity acid gas stream without sacrificing flame stability. Because of these criteria, modifications to the conventional process are often required, resulting in a modified Claus process. For the studies discussed here, these modifications include the use of a 95% pure oxygen stream as the oxidant, a split flow configuration, and the preheating of the feeds with the intermediate pressure steam generated in the waste heat boiler (WHB). In the future, for IGCC plants with CO2 capture, the Claus unit must satisfy emission standards without sacrificing the plant efficiency in the face of typical disturbances of an IGCC plant, such as rapid change in the feed flow rates due to load-following and wide changes in the feed composition because of changes in the coal feed to the gasifier. The Claus unit should be adequately designed and efficiently operated to satisfy these objectives. Even though the Claus process has been commercialized for decades, most papers concerned with the modeling of the Claus process treat the key reactions as equilibrium reactions. Such models are validated by manipulating the temperature approach to equilibrium for a set of steady-state operating data, but they are of limited use for dynamic studies. One of the objectives of this study is to develop a model that can be used for dynamic studies. In a Claus process, especially in the furnace and the WHB, many reactions may take place. In this work, a set of linearly independent reactions has been identified, and kinetic models of the furnace flame and anoxic zones, WHB, and catalytic reactors have been developed. To facilitate the modeling of the Claus furnace, a four-stage method was devised so as to determine which set of linearly independent reactions would best describe the product distributions from available plant data. Various approaches are taken to derive the kinetic rate expressions, which are either missing in the open literature or found to be inconsistent. A set of plant data is used for optimal estimation of the kinetic parameters. The final model agrees well with the published plant data. Using the developed kinetics models of the Claus reaction furnace, WHB, and catalytic stages, two optimization studies are carried out. The first study shows that there exists an optimal steam pressure generated in the WHB that balances hydrogen yield, oxygen demand, and power generation. In the second study, it is shown that an optimal H2S/SO2 ratio exists that balances single-pass conversion, hydrogen yield, oxygen demand, and power generation. In addition, an operability study has been carried out to examine the operating envelope in which both the H2S/SO2 ratio and the adiabatic flame temperature can be controlled in the face of disturbances typical for the operation of an IGCC power plant with CO2 capture. Impact of CO2 capture on the Claus process has also been discussed.