Experiments have been carried out to analyze the characteristics of laminar cross-flow methane-air diffusion flames in the presence of bluff bodies. The stable operating regime having steady and oscillating flames, and unstable operating regime that includes flame blow-out and extinction, are identified by varying the air and fuel flow rates systematically. Detailed stability maps indicating these regimes have been proposed for bluff bodies having rectangular, isosceles triangular and semicircular shapes. Three types of flames, namely plate stabilized, bluff body stabilized and separated flames, have been captured using a high-definition digital camera. The flame anchoring locations, flame shapes and transitions between different regimes of stabilization have been analyzed thoroughly. Hysteresis effects in the transition between the regimes, when the air flow rate is systematically increased or decreased, are also presented in the stability maps. The interesting features of the semicircular cylinder bluff body have been discussed in comparison to other two bluff bodies. Additionally, the effect of addition of hydrogen in small quantities to methane has also been envisaged. When 10% hydrogen by volume is added to methane, the plate stabilized regime is seen to be widened. Also, the hysteresis effect is seen to reduce with the injection of hydrogen. © 2016 Elsevier LtdAll rights reserved.