In this chapter we describe in some detail the solution algorithms used to solve steady-state and transient problems for the reactor types described in previous chapters. The proprietary steady-state solver, Twopnt, is described in more detail, while the transient solvers have been primarily developed by 3rd -party organizations and are documented elsewhere in order to provide insight into the diagnostic messages and solution procedure. Several of the transient solvers employed by Ansys Chemkin are available in the public domain. In such cases, the source code is included in the Chemkin installation and this code usually includes detailed explanation of the solver usage as comments in the FORTRAN code. A discussion of which transient solver is used for each class of reactor models and references to those solvers are generally included in the previous reactor-model chapters. For steady-state problems, however, some common characteristics of the solver approach are discussed here.