The first significant refraction arrival through a thin high-velocity elastic layer in an elastic medium has been investigated theoretically by means of an asymptotic theory. This first low-frequency arrival is closely connected with the longitudinal plate wave in the thin layer. When the medium surrounding the layer is a fluid, the signal does not decay exponentially with horizontal distance; when the surrounding medium is a solid, the signal does decay exponentially. A very simple approximate formula for this exponential decay is presented and compared with numerical results of the more rigorous theory. The decay as well as the shape of the signal is dependent upon the contrast in elastic parameters between the plate and the surrounding medium. Higher-frequency early arrivals, associated with the second symmetric mode, have also been investigated. They exhibit greater exponential decay with horizontal distance than the low-frequency first arrivals.