Numerical bifurcation techniques were analyzed and developed for studying the multiplicity of the 2-D model of the catalytic porous wall reactor with axial flow. The continuation technique is based on the generalized inverse iteration with Rayleigh quotient. The using of the multigrid and the conjugate gradient for nonsymmetric systems methods in the continuation algorithm is tested. The choice of the preconditioner is also analysed for the conjugate gradient methods. The numerical performances of the different algorithms used are investigated and compared. The key parameter of the investigation is the reaction parameter. The effect of the other parameters on the bifurcation behaviour is briefly analyzed.