An ultrasonic technique for a simultaneous determination of traveling times and acoustic impedances of three-layered, platelike specimens using a normally incident longitudinal wave is presented. The acoustical properties are determined by minimizing the difference between measured and calculated resonant frequencies in the well-known least-squares sense. The resonant frequencies of the layered structure are deduced, in transmission, from the maxima of the magnitude of the transmission spectrum, or, in reflection, from the pi values of the phase of the reflection spectrum. Measurements are carried out in the frequency range 1-20 MHz for steel/aluminum/steel and silver/copper/nickel specimens with individual layer thickness values ranging from 0.3 mm to 2 mm. The differences between the inverted thicknesses and those measured directly with an optical microscope range from -4 microm to +13 microm. Estimated error bounds suggest that the inverted travel times are accurate within +/- 1 ns with 95% probability.