This chapter focuses on the formation of the second-order process zone at the tip of a mode I crack. We begin with a rigorous analytical investigation, deriving the exact eigenfunction solution for the auxiliary equation. This analysis offers precise insights into key characteristics of the zone, including its spatial distribution, size, form factor, and propagation dynamics. Complementing the analytical framework, we use simulations to explore the bifurcation behavior of the process zone across a range of parameters. We construct a phase diagram that demonstrates strong agreement with analytical predictions. Together, these approaches provide a comprehensive understanding of the second-order process zone’s formation and behavior at the mode I crack tip.