Abstract-Combustion in vortex flow fields is of interest in fundamental studies and also because it occurs in many practical situations. Some important analytical contributions to this topic are due to Marble and his students. The Marble problem of a viscous core vortex interacting with a non-premixed flame is treated in the present paper. The analysis is numerical, Detailed calculations of the flame structure are performed.Results obtained confirm intuitive aspects of Marble's analysis. The growth of the core of products is examined. Similarity laws for the radius of this core and for the global reaction rateare verified. Influences of equivalence ratio and Reynolds number are illustrated and discussed.