Detailed kinetic models (DKMs) have evolved considerably over the past two decades, in several cases becoming the kinetics kernels of complex process models for industrial applications. In the previous chapters, we discussed in detail how to construct automatically a rigorous and useful reaction network for complex process chemistries (Chapter 3) and how to organize and evaluate rate constants for each reaction in the reaction network (Chapter 4). In the context of the complete model building work process as discussed in Chapter 1, the model building stage is now fully automated and thus is no longer the rate-determining step; often, the model tuning process, which involves repetitive solution and optimization stages, becomes more time consuming. This is especially so if an off-the-shelf numerical package is used without consideration of the type of kinetic model. In this chapter, we will focus on the fast and efﬁcient solution of detailed kinetic models from both the mathematical and the chemical and physical points of view. We will illustrate how the nature of the chemical problems and reaction kinetics provide insights to improve the model solving techniques and thus speed up the model development process as a whole.