Abstract: A variational expression of angular frequency ω² is proposed for surface acoustic waves propagating on both free and metallized surfaces of piezoelectric crystals. From this expression an analytical solution for SAW piezoelectric coupling ceofficient, K², can be derived as a function of piezoelectric crystal constants. Comparison of the variational evaluations of K² with the exact data obtained by computer iterative algorithm shows the applicability of this expression as a guidance for estimating K² of piezoelectric crystals. Furthermore, by means of the combination of this expression with the coupling-of-modes theory, the analysis of the shorted-circuit metal strip grating can be significantly simplified. The SAW reflectivity of a single strip in the grating will be cast into closed form functions of material constants and strip geometric parameters. The result of reflectivity correctly explains the published experiments and, in particular, the phase behavior of reflectivities of different strip film and substrate configurations. The numerical results of reflectivities are in agreement with the published experimental data.