This chapter includes solidification of binary alloys, focusing on substitutional and interstitial types with a solute concentration of \(C_{o}\) . The chapter explores the heat transfer during solidification, examining it as either thermal conduction or a coupled heat and mass transfer process at the solidifying interface. Mathematical modelling relies on finding analytical solutions to one-dimensional heat equations within a semi-infinite domain. The chapter introduces the analytical procedure for solving solidification problems in rectangular geometries, considering thermal resistances in the mould, solid, and melt. The solidification velocity, a measure of the interface movement, is also addressed. These analytical solutions provide insights into the formation of solute boundary layers at the liquid-solid interface, which is treated as a smooth, planar front. Similarity solutions, based on specific assumptions about the solidification model, are employed. Temperature and solute concentration field equations are derived to understand their influence on the process. The chapter also includes the theoretical possibility of amorphous solidification, where rapid cooling prevents crystal formation. However, the focus remains on crystalline solidification of binary alloys, introducing relevant analytical models for characterizing the process under equilibrium conditions.