In the first part of this work, a new ytterbium selective PVC membrane electrode based on 1,10-phenantroline-5,6-dione (PDO) as a neutral ionophore was constructed. The electrode showed a Nernstian response for Yb(III) ions over a wide concentration range of 5.0 × 10 -6 to 1.0 × 10 -2 M with a slope of 19.7 mV/decade. The other performances of this electrode were low detection limit (5.7 × 10 -7 M), very short response time ( 5 s ), a life time of over 1.5 months, and wide working pH range (4.0-12.0). The theoretical calculations of the Yb(III) and other cations with ionophore were performed by the semiempirical PM6/Sparkle method. It indicated high selectivity for Yb(III) in comparison with alkali, alkaline earth and heavy metal ions. This sensor was successfully used as an indicator electrode in potentiometric titration of Yb(III) ions with EDTA. It was also applied in determination of fluoride ion in the two mouth wash samples. In the second part of this work, an europium(III) selective PVC membrane electrode based on 4-methylphenylisothiocyanate (4-MePIC) as a neutral ionophore was constructed. This sensor exhibited a Nernstian response for Eu(III) ions over a wide concentration range of 1.0 × 10 -6 to 1.0 × 10 -2 M with a slope of 19.7 mV/decade. The detection limit was 1.2 × 10 -6 M and the response time was ( 6 s) and could be used for at least 1.5 months in the wide working pH range of 3.0 – 9.5. This membrane electrode was also used as an indicator electrode in potentiometric titration of Eu(III) ions with EDTA and also applied successfully in determination of fluoride ion in the two mouth wash samples. The PM6/Sparkle calculations were also performed for this electrode.