Prediction of the flow through cascades of blades is fundamental to all aspects of axial-flow compressor aerodynamic design and analysis. Although the flow through the annular cascades of blades in a compressor is really a three-dimensional flow problem, there are many advantages to considering the simpler problem of two-dimensional flow in cascades. It offers a very natural view of cascade fluid dynamics to make it easier for designers to develop an understanding of the basic flow processes involved. Indeed, very simple two-dimensional cascade flow models were used in this educational role long before computational methods and computers had evolved enough to produce useful design results. Today, blade-to-blade flow analysis is a useful design and analysis tool that provides reasonable approximations to many problems of interest. Inviscid blade-to-blade flow analysis addresses the general problem of two-dimensional flow on a stream surface in an annular cascade, as discussed in Chapter 3. Two-dimensional boundary layer analysis can be used to approximate viscous effects. Although very useful, this approach does have limitations. It ignores secondary flows that develop from the migration of low momentum boundary layer fluid across the stream sheet. It also loses accuracy when significant flow separation is present. This chapter considers theoretical methods to model two-dimensional blade-to-blade flow. The next chapter considers a different approach to the problem, where empirical models are derived from two-dimensional cascade test data. The methods presented in this chapter are basically the same as those presented in Aungier (2000), but are adapted to conventions more commonly used for axial-flow compressors. Aungier (2000) provides detailed guidance relative to implementation of the methods in numerical analyses that is not repeated here. Readers interested in those details should consult the original reference.