A numerical model is developed to simulate the wrinkled laminar flame sheet flapping in weakly turbulent premixed combustion. The wrinkled laminar flame sheet is represented by a discrete distribution of volume sources called source disks. These source disks are utilized to produce the acceleration of combustion products behind the flame sheet. The laminar flame speed is allowed to vary according to flame stretch. A modified source model is proposed against the background of the existing source model's physically unrealistic symmetric expansion in both the upstream and the downstream directions. This flame model also includes flame-generated vorticity which is associated with the increasing entropy intrinsic to any system going through an irreversible process. The flame-generated vorticity is treated as discrete vortex disks. Vorticity created on the surface of the flame holder is computed with the vortex sheet method and diffuses into the surrounding flow in the form of vortex disks. The freestream turbulence is simulated by injecting vortex disks into an initially uniform freestream. Flame-flow interactions are studied when a thin circular cylinder, a large circular cylinder, and a flat plate normal to freestream are used as flame holders. Results sho\v that the modified source model gives more accurate prediction of flame angle than the existing source model does, the relative errors can be reduced by as much as four times. The modified source model also produces velocity profiles closer to those found in experiment, the deviations are cut by half at most sampling points in the flow. The vorticity shed from a thin circular cylinder flame stabilizer is found to only influence downstream regions very close to the cylinder. The eddy shedding behind a bluff body flame holder is suppressed in reacting flow simulations and the computed recirculating zone in a reacting flow is nearly half as long as that in a cold flow. When the relative size of the flame holder is one order of magnitude larger than the thickness of flame sheet, the vorticity shed by the flame holder can no longer be neglected. Flame wrinkling and flame extinction caused by vortical fluid motion behind the flame holder are found through numerical simulation. / Ph. D.