It has been previously shown that thermal expansion may have a role in a boundary layer flashback of premixed turbulent flames [Gruber et al., J Fluid Mech 2012], enhancing the flame velocity through flame corrugation. The current study focuses on the two-dimensional numerical investigation of the interaction of a periodic shear flow and a laminar premixed flame. The periodic shear is a simplified model for the oncoming prolonged velocity streaks with alternating regions of high and low velocities found in a turbulent channel flow close to the wall. The parametric study focuses on the amplitude and wavelength of the periodic shear flow, and gas expansion ratio. It has been found that with the increase of the amplitude of the periodic shear flow, as well as the gas expansion, the curved flame velocity increases monotonically. The flame velocity dependence on the periodic shear wavelength is non-monotonic, which is consistent with previous theoretical studies of the curved premixed flame velocity.