A connection between the process conditions and the morphology of the melt-crystal interface has been sought by studying a simple batch type directional solidification model. Our model is based on the continuum diffusion equations for the heat and mass transport with both the buoyancy force effect and the solute diffusion effect in solid phase being neglected. The dynamical behavior of the interface has been investigated by the linear stability analysis and the boundary integral equation method. The results from the linear stability analysis show that the interface is stable to the infinitesimal disturbances superposed on the flat interface in both cases of pure melt and melt with solute. It is also found from the numerical results that the stability of the interface is extended even to the finite size disturbances.