Interactions of fuel-rich and fuel-lean mixtures and formation of interlinked multiple flame zones are observed in gas turbines and industrial furnaces. For fundamentally understanding such flames, numerical investigation of heat and mass transport, and chemical reaction processes, in laminar, counter flowing partially premixed rich and lean streams of methane and air mixtures, is presented. An axisymmetric numerical reactive flow model, with C2 detailed mechanism for describing methane oxidation in air and an optically thin radiation sub-model, is used in simulations. The numerical results are validated against the experimental results from literature. The equivalence ratios of counter flowing rich and lean reactant streams and the resulting strain rates have been varied. The effect of these parameters on the flame structure is presented. For a given rich and lean side equivalence ratios, by varying the strain rates, triple, double and single flame zones are obtained.