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ZnWO4 single crystals both undoped and doped with various concentrations of Yb3+ and Li+ ions have been grown. The actual concentrations of dopants have been measured by atomic emission spectroscopy with inductively coupled plasma, as well as by polarized optical absorption spectroscopy. The segregation coefficients of the dopants between the crystal and melt have been evaluated. Hardness and fracture toughness of the crystals were measured by indentation method. The dependencies of the measured values on the dopants concentrations were analyzed. The optimal dopants concentrations, providing the best mechanical strength of Yb,Li:ZnWO4 crystal have been found.