A two-dimensional adaptive finite-element code is used to numerically investigate the propagation of a laminar premixed flame in a closed rectangular chamber giving rise to the so-called tulip instability. The physical model includes a single one-step chemical reaction where the physical parameters involved in the model are chosen in order to adequately represent a stoichiometric methane-air flame. Attention is focused on the shape of the flame and the flowfield generated by the combustion process. A detailed comparison between the numerical results and available experimental data shows a very good agreement, for various sizes of the combustion chamber.