The interaction of a premixed methane/air flame with flow unsteadiness is studied computationally using a stagnation-point flow configuration. The problem is of fundamental interest and also relevant for turbulent combustion in the laminar flamelet regime. In the present study, of particular interest is the flame residing in a weakly strained flow field such that the flame is stabilized away from the viscous boundary layer adjacent to the stagnation plane and is free to move in response to flow perturbations. An unsteady sinusoidal strain rate field is imposed on the flame, and an extensive parametric study is conducted by varying the frequency and amplitude of strain rate fluctuation. It is found that for high frequencies and large amplitudes, flow direction reverses upstream of the flame, thereby establishing a new stagnation plane in the preheat zone ahead of the flame. This observation indicates that the flame strongly affects the upstream flow field and could also possibly explain the reported occurence of flow reversal in experimental studies of turbulent jet flames. Effects of other key parameters such as the Lewis number, mean flame speed, and gas expansion ratio on flame-flow interaction and flow reversal are studied by investigating highly lean (Le < 1) and rich (Le > 1) hydrogen/air flames. The physical mechanism responsible for flow reversal phenomenon is explained.