The (isothermal) eutectic solidification structures of binary alloys have been simulated using a twodimensional monte carlo model. The model takes into account simultaneous diffusion of all liquid atoms, incorporates the energy contributions of like and unlike nearest and next-nearest neighbor bonds in the solid on solidification, and allows surface rearrangement at the solid-liquid interface. It has been demonstrated that results obtained from this model exhibit phenomena observed during eutectic solidification in practice, for example, the passage of the growth rate through a maximum upon decreasing temperature. Particular attention has been devoted to the effect of growth parameters, such as the next nearest neighbor interaction in the solid and the surface relaxtion length, on the morphology of the growing solid phase.