This study introduces a reliable method for simultaneously determining the thickness, slope, and ultrasonic velocities of slope plates using laser ultrasonic techniques without any damage in the thermoelastic regime. The method involves solving a system of equations to determine the arrival times of multiple signals displayed on a waveform. Numerical simulations indicate that the velocity of the skimming longitudinal wave remains constant when the Rayleigh wave does not overlap with its signal. Consequently, a prediction model for aluminum alloy has been established, enabling the estimation of the constant ratio between the velocities of skimming longitudinal and bulk longitudinal waves based on the skimming longitudinal velocity obtained by scanning the generating laser along the material's surface. This ratio, approximately 0.950, facilitates the combination of the skimming longitudinal wave with the reflected and mode-converted waves from the specimen's back surface to deduce the desired parameters. The method successfully determined the thickness, slope, and wave velocities of several specimens with slopes ranging from 0% to 1.96% and a maximum thickness of about 10 mm. Evaluating the influence of the size of the disk ultrasound source produced by the unfocused laser beam, we found that the radius of the disk source should be considered when calculating the arrival time of the skimming longitudinal wave. The root mean square deviation in measuring thickness, slope, longitudinal wave velocity, and shear wave velocity were approximately 0.100 mm, 0.10 %, 70 m/s, and 20 m/s, respectively. An assessment of the measured results, based on the root mean square deviation and uncertainty across all specimens, demonstrates the practical feasibility of the proposed method