Directional coarsening in binary alloys during phase separation has been simulated by means of the Monte-Carlo technique based on the spin-exchange Ising model in two-dimensional squared lattices. A uniaxial interaction has been imposed on the Hamiltonian of the standard Ising system in order to achieve directional coarsening of the domained structure. Characterization of the domained structure with the snapshot patterns, the spatial correlation function and the structure function, is also given. It has been found that with time this system exhibits highly uniaxially anisotropic patterns of the domain morphology and the correlation function, and also achieves a uniaxially textured structure function. Under such a uniaxially anisotropic interaction, the dynamics of the system still achieves a good agreement with the dynamic scaling hypothesis. Towards the later stage, the kinetics of coarsening acquires a growth exponent of 1/3, the same as the well-known value in the isotropic alloys.