Abstarct: Solidification occurs in many industrial processes such as casting and welding. The macro-scale physical properties of the solidified material depend on its micro-scale structure. The product micro-structure during solidification is largely dependent on several factors such as cooling rate, temperature gradient at the interface, surface tension and interface velocity. We need to control the solidification processes in order to assure the quality and reliability of the solidified product. The solid-liquid interface velocity in pure material solidification and mushy zone thickness in alloy solidification are the most important factors which affect the product micro-structures and quality. The main objective of this research is the control of the above mentioned parameters to reach the desired material quality during solidification of pure and alloy materials. Thus, it is essential to compute the boundary conditions which lead to desired interface velocity and mushy zone thickness. These problems are classified in the Inverse Heat Transfer Problems (IHTP). The effect of mushy zone thickness is ignored in all previous researches subject to the application of IHTP in solidification processes. The mushy zone is a two phase region with solid fraction dependent (temperature) properties. The main goal of the thesis is to control the mushy zone thickness using IHTP. The objective function is defined baxsed on the difference between desired and computed temperatures at the interface and minimized by Conjugate Gradient Method (CGM). The enthalpy formulation is used to avoid solving the inverse problem for three regions respectively. The numerical simulation is validated by applying a known boundary heat flux and recording the temperatures inside the domain. Then, this is used for solidification control in one and two dimensional problems. The numerical results show that the mushy zone thickness, shape and the material quality can be controlled by applying two control heat fluxes at the both mold sides, simultaneously. The obtained heat fluxes to control constant and variable mushy zone thicknesses showed that only cooling is required on solid side and both cooling and heating on liquid side, depending on the mushy zone thickness. Thus the obtained results can be used in many related industries to improve the solidified material quality.