The safety issues in hydrogen production, storage, transportation, and utilization have caused a high level of concern. Flame acceleration stimulated by the rigid obstacles has been much more addressed, while little attention has been paid to the cases with the flexible obstacle, which exists popularly in explosion scenarios. In this paper, a series of experiments was conducted to study the effect of the flexible/rigid obstacle on the flame front and pressure evolutions with varying equivalence ratios. Results show that the gas flow ahead of the flame pushes the flexible obstacle to tilt, which induces a smaller gap inlet between the tube wall and the top of the obstacle and more significant shear layer and vortex. These, together with its rough surface, influence the flame shape, the transition of the flame from a laminar flame to a turbulent flame, the instability in the flame interaction with the shear layer, etc. Consequently, flame acceleration is significantly less pronounced for the flexible obstacle than that for the rigid obstacle. The flexible obstacle always decays the pressure in the upstream region of the obstacle with varying equivalence ratios. However, with regard to the pressure in the downstream region, the damping effect can be found for the equivalence ratio of 4.0 but disappears for 0.6 and 1.0.