Spin-wave excitations in finite rectangular elements of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ni</mml:mi><mml:mn>80</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Fe</mml:mi><mml:mn>20</mml:mn></mml:msub></mml:mrow></mml:math>

A Brillouin light scattering study and theoretical interpretation of spin-wave modes in arrays of in-plane magnetized micron-size rectangular ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ elements are reported. It is shown that two-dimensional spin-wave eigenmodes of these elements can be approximately described as products of one-dimensional spin-wave eigenmodes of longitudinally and transversely magnetized long finite-width permalloy stripes. The lowest eigenmodes of rectangular elements are of dipole-exchange nature and are localized near the element edges, while the higher eigenmodes are of a mostly dipolar nature and are weakly localized near the element center. The frequency spectra and spatial profiles of these eigenmodes are calculated both analytically and numerically, and are compared with the results of the Brillouin light scattering experiment.