We study the properties of the combustion of pure neutron matter into strange matter in the framework of relativistic hydrodynamical theory of combustion. Because of the uncertainties in the actual properties of neutron matter, we employ the free neutron, Bethe-Johnson, Lattimer-Ravenhall, and Walecka equations of state and for strange matter we adopt the MIT bag model approximation. We find that combustion is possible for free neutron, Bethe-Johnson, and Lattimer-Ravenhall neutron matter but not for Walecka neutron matter. We interpret these results using a simple polytropic approximation showing that there exists a general flammability condition. We also study the burning of neutron matter into strange matter in a pipe showing that hydrodynamics demands flames faster than predicted by kinetics by several orders of magnitude, implying that the flame must be turbulent. Also the conditions for the deflagration to detonation transition are addressed, showing that in a pipe some of them are satisfied, strongly suggesting that the actual combustion mode should be detonation.