The disclosure relates to a measurement of the wall thickness of samples such as pipes, containers or panels in which the interior or underside is inaccessible and to a measurement of the layer thickness of coatings or linings of the samples. Disclosed are special measuring arrangements using ultrasonic transmitters and ultrasonic receivers with pitch-catch and pulse-echo configurations, and the associated method for determining the wall thickness without prior knowledge of the sound velocity in the sample. Measuring individual layer thicknesses of a multilayered system without prior knowledge of their sound velocities is also disclosed. The method and the measuring arrangement allow the wall thickness to be measured independently of the knowledge of the sound velocity of the sample. This reduces the measurement uncertainty for the wall thickness and inner diameter of the pipe and thus reduces the measurement uncertainty for a clamp-on ultrasonic flow meter.