A computational procedure for the hydrodynamic analysis and design of horizontal-axis tidal turbines is presented and numerical applications are discussed. The methodology combines an original design algorithm and a turbine hydrodynamics model valid for arbitrary 3D flows. Different from standard design methods based on blade element models, 3D-flow corrections are not necessary. Blade geometry parameters are determined with the objective to maximize power at given design Tip Speed Ratio (TSR), whereas a constraint is introduced in order to limit turbine thrust at TSR higher than the design condition. Numerical applications include the design of a laboratory scale turbine and a full-scale turbine for the exploitation of tidal streams in the Messina strait. Alternative design solutions obtained by varying the design tip speed ratio are compared in terms of energy output as well as mechanical loads transferred to the powertrain.