A theoretical description of free surface motion is presented for a semi-infinite unbounded smectic-A (Sm-A) liquid crystal. The characteristic equation is analyzed in a wide range of frequencies and wave numbers. It is shown that at low frequencies the surface eigenmotion is a wave of the second sound type. The wave velocity is twice that of the maximum second sound velocity in the bulk phase. This Rayleigh mode may be excited and detected as surface transverse waves. At high frequencies the surface eigenmotion is a damping viscous mode. The spectral intensities of the surface displacement fluctuations are presented in rather simple form for separate areas of wave numbers and frequencies. These results may be used to describe light scattering experiments. It is shown that the surface tension is negligible when describing Sm-A surface eigenmotions, in contrast to ordinary liquids. At the same time the surface tension is sufficient for surface displacement fluctuations at low frequencies.

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