A numerical scheme is presented for classifying the different static bifurcation behaviors exhibited by a nonlinear system in its remaining parameter space. This numerical technique differs from previously published schemes in that the application of singularity theory is done numerically and requires no explicit differentiations of the system in question. It also does not require the reduction of the mathematical model to a scalar equation. The utility of this multivariable scheme will be demonstrated through an application to a seven PDE tubular packed-bed reactor model.