Large Eddy Simulations (LES) of turbulent lean-premixed flames of V- and M-shape are presented. A simple algebraic closure with the ability to capture finite-rate chemistry effects is used for subgrid reaction rate modeling. The V-shaped flame is stabilized in the inner shear layer between a swirling annular jet and a central recirculating bubble in a sudden expansion duct. The M-shaped flame is stabilized in the inner and outer shear layer, adjoining the corner recirculation zone induced by the vertical step. The focus of the study is on the flow fields and shapes of the flames, which distinguish themselves through different heat load and sensitivity to local extinction. Good agreement with measurements is observed for the cold and the reacting flow cases. The numerical results suggest that the entrainment of hot gases into the outer recirculation zone occurs close to the impingement point of the swirling annular jet on the wall and this process is strongly dependent on intense vortical structures in the outer shear layer. The results further suggest that local extinction influences the position of the flame in the inner shear layer and, thereby, also the intensity of the local entrainment process.