An ultrasound process and apparatus for determining the location of an ultrasonic homogeneity discontinuity called parietal surface situated in a tissue from a radio-frequency signal (y(z)) function of digital depths along an excitation line (Z) crossing said parietal surface, comprising steps of: filtering the radio-frequency signal in order to provide a tissue signal (e(z)) representative of tissue scatterers, apart from a radio-frequency excitation signal; filtering the tissue signal (e(z)) in order to provide a variance amplitude signal (S(z)) as a function of the digital depths on the excitation line wherefrom the corresponding parietal surface digital depth is determined. This process is used to estimate an artery radius from the digital depths of the arterial walls on the excitation line.