The morphological transitions of shallow cells near. the onset of Mullins-Sekerka instability during the thin-film directional solidification of a succinonitrile/acetone alloy have been simulated quantitatively by means of phase field modeling for the first time. Long time/length scale experiments at a constant pulling speed were performed for the purpose of comparison. The simulation results show good agreement with classic theories in the planar and lambda(c)<->lambda(c)/2 cellular bifurcation regions, where lambda(c) is the critical wavelength. At a higher pulling speed, V, an anti-trapping current was introduced to maintain the local equilibrium, and the region for V lambda(2)similar to constant was found. Finally, multiplets appeared when lambda was close to lambda(c)/4. In the experiments, due to slow solute accumulation in the molten zone, morphological transitions were also revealed. Some interesting nonlinear phenomena, such as tip splitting, coarsening, pinch-off, and asymmetric cells, were also confirmed through both simulations and experiments.