In this paper, the development of frontal polymerization under conditions of free convective motion of a reactive mixture is studied experimentally and numerically. The convection is caused by the reaction exothermicity and by the density change, because the polymer is more dense than the monomer. The propagation of polymerization fronts with convection is studied for the photoinitiated polymerization of an aqueous solution of acrylamide. Comparison of terrestrial and space experiments with the results of numerical simulation shows that convection can lead to the formation of inhomogeneities in the polymer product; it can change the speed of propagation of the reaction front and even change the reaction from frontal to volumetric.