Due to its strong exothermicity and strong reactant inhibition, the FTS is a great candidate for employing a crossflow reactor, in which the reactants are distributed along the reactor. The desired temperature, which is 480-500 K on a Co catalyst, aimed to achieve reasonable conversion with reasonable selectivity, is achieved by cooling, either by using a diluent by inert or by using a heat exchanger. The main features of the CFR for generic kinetics like 1st order exothermic reaction, were analyzed and published by our group. Here we apply this design for FTS on a Co catalyst using a published kinetics based on a L-H mechanism coupled with an Anderson-SchultzFlory kinetic model for high hydrocarbons to show the advantages gained-better activity and selectivity-since most of the reactor is operating at fixed conditions, unlike the PBR. The analysis follows several steps: (i) analysis of multiplicity of homogeneous states; (ii) analysis of the steady state spatial solution and plot of the domain of attraction of the active state; (iii) analysis of the full 1-D dynamic model, showing travelling-fronts or travelling- pulses, that may exit the system, as well as stationary-pulse solutions. In conclusion we note that the CFR offers many advantages at the expense of a more complex reactor structure: In the discussion we analyze the implications of the various parameters (mass-and heat-transfer) and the implications of the assumptions made in the model and conclude that the parameters are realistic.