The temperature distribution, geometry and size of the melt pool, and solidification parameters were computed using the heat transfer and material flow model for the directed energy deposition process. The thermal cycle and melt pool size were computed for different process parameters such as laser power, deposition speed, and laser beam radius across the multiple layers for deposition of Al-0.5Sc-0.5Si alloy. The computed thermal cycles at various locations from the centerline and melt pool size showed fair agreement with the experimentally measured result. The computed thermal gradient and solidification rate were mapped over the solidification map, which was in agreement with the experimentally observed microstructure. The transition in solidification morphology with varying melt pool depth and process parameters were fairly observed inside the melt pool. The fraction of equiaxed solidification morphology increases with the reduction in a thermal gradient.