The classical point model of a crack [1] is valid only for cracks of widths exponentially small compared to the plate thickness: kW ≪ exp(-(kh)^-8/5), where W is the crack width, h is the plate thickness, and k is the wave number. Therefore, generally speaking, the results obtained earlier for some systems with cracks should be reconsidered in terms of an improved model [2]. This paper presents the corresponding study of the edge waves described earlier for the case of an infinitely narrow crack [3]. A numerical study of the dispersion equations is performed for the wave numbers of symmetric and antisymmetric edge waves with different parameters of the plate-liquid system.