The present study numerically investigates the propagation of a laminar premixed flame front in two-dimensional tubes with a sudden contraction and isothermal cold walls. Navier-Stokes equations and species equations are solved with a single-step overall reaction model for a stoichiometric propane/air mixture. The finite volume method is applied in investigating flame behavior during the passage through a sudden contraction in tubes of various diameters. These investigations show that a flame can enter a smaller diameter tube from a wider one and propagate in a stable manner in all configurations of diameters of both tubes as long as the diameter of the narrow tube is far from the quenching diameter. By decreasing the diameter of the narrow tube, we approach conditions where the dimension of the wide tube decides if the flame will propagate or quench. This is associated with a temporarily increased ratio of heat losses to thermal energy generation caused by a greater heat loss area. It is also shown that a tulip-shaped flame occurring at large diameters of the wide tube is particularly exposed to quenching during propagation through the sudden contraction. This is due to a transition from a tulip-shaped flame to a mushroom-shaped one, which takes place at the entrance to the narrower tube.