Transition metal nitrides can be synthesized in the combustion regime using a self-propagating, high-temperature synthesis by the process of filtration combustion. A detailed two-dimensional numerical study for the filtration combustion process in the cross-flow configuration is presented. The process is modeled by a two-dimensional pseudohomogenous model. The model equations, which are very stiff and exhibit varying time and length scales, are solved using finite differences on a two-dimensional orthogonal adaptive mesh. The effects of pressure, bed height and bed porosity on combustion front propagation and final conversion are studied. A series of full simulations for the titaniumnitrogen system shows good agreement between theoretical predictions and experimental observations.