Measurement accuracies of leaky surface acoustic wave (LSAW) velocities for materials with highly attenuated waveforms of VðzÞ curves obtained by the line-focus-beam ultrasonic material characterization (LFB-UMC) system are investigated. Theoretical investigations were carried out and experiments were performed for TiO 2 -SiO 2 glass (C-7972), Li 2 O-Al 2 O 3 -SiO 2 glass ceramic (Zerodur Ò ), and (111) gadolinium gallium garnet (GGG) single crystal as specimens. Waveform attenuations of VðzÞ curves for C-7972 and Zerodur Ò are greater than those for the (111) GGG single crystal. Frequency dependences of the waveform attenuations were calculated for each specimen by considering the propagation attenuation of LSAWs. The theoretical results revealed that the waveform attenuation dominantly depends upon the acoustic energy loss due to the water loading effect on the specimen surface, and that the waveform attenuation becomes smaller with decreasing frequency. Significant improvement of the measurement precision of LSAW velocities was demonstrated for each specimen using three LFB ultrasonic devices with different curvature radii R of the cylindrical acoustic lenses: R ¼ 2:0 mm at 75 MHz, R ¼ 1:5 mm at 110 MHz, and R ¼ 1:0 mm at 225 MHz; for C-7972, the precisions were improved from AE0:0053% at 225 MHz to AE0:0020% at 75 MHz.