Today gas turbines are subject of continuous studies aimed at optimizing performances, safety, reliability and efficiency. The current activity is carried out by a collaboration between the Politecnico of Torino and Ethos Energy Italia S.p.A., independent service provider working in the gas turbine field, operating also in design, maintenance and repair. The purpose of this thesis is to model leakage losses in correspondence of a gas turbine 1^st stage between stator and rotor, and to optimize the casing of the stator unit with the aid of\textit{ grooved shroud}, through Computational Fluid Dynamic (CFD) simulations. The grooved shroud, consisting of precisely engineered channels on the shroud surface, aims to control tip leakage flow and reduce mass flow losses.