Large dendritic single crystal blades operating in jet engines or land-based turbines are commonly produced in industrial plants. However, the production cost of some of these parts remains high due to the several types of defect which may appear during the different stages of the investment casting process. The prevention of stray crystal formation during solidification is the main problem which has to be faced by engineers. Analytical developments are first presented in order to define conditions under which single crystal growth is favored. This process window is described in a space where the thermal gradient and the withdrawal speed of a Bridgman furnace apparatus are the controlling parameters. The limits of this process window are then refined in order to determine the influence of other parameters such as the crystallographic orientation of the single dendritic grain, the size of the platform in which the single grain has to extend, the growth kinetics of the dendrite tips, or the existence of a lateral thermal gradient.