The analysis of a chemical reactor by numerical bifurcation techniques can completely define the multiplicity and stability of its equilibrium states and can give insights into the reactor's parametric sensitivity and dynamical behavior in the neighborhood of the chosen operating points. In this paper, we will present some of the numerical bifurcation techniques used and developed in analyzing an autothermal packed bed tubular reactor. The bifurcation behavior found will be cataloged over the range of relevant reactant inlet conditions, and an explanation for the isolated solution branches characteristic of this reactor will also be presented.