This chapter focuses on the solidification of A-B binary alloys with a specific solute composition ( \(C_{o}\) ). Understanding a binary phase diagram is important, as it defines the resulting solid phases, their compositions, and the presence of undercooling ( \(\Delta T\) ) based on the alloy’s composition and the solidification velocity. Assuming equilibrium solidification at a low velocity, the chapter explores analytical methods to solve eutectic solidification problems. The focus is on the formation of regular \(\alpha \) - \(\beta \) lamellar structures, a consequence of the eutectic reaction, \(L\rightarrow \alpha +\beta \) , that releases latent heat of fusion. This reaction defines “eutectic solidification”, where the alloy’s composition ( \(C_{\alpha }\leq C_{o}\leq C_{\beta }\) ) falls within the eutectic range. The analysis assumes minimal undercooling and steady solidification with slow \(\alpha \) - \(\beta \) interface advancement, heavily influenced by local diffusion mechanisms (lateral and axial) within the solidification plane. The lateral diffusion, associated with the contoured \(\alpha \) - \(\beta \) interface, is considered an oscillatory process.