A method for tissue characterization by ultrasound wave attenuation measurements is provided that comprises: a) transmitting at least an ultrasound pulse in a target body; b) receiving ultrasound pulses reflected by the target body and transforming the reflected ultrasound pulses into RF reception signals; c) extracting an envelope of the received RF signals; d) carrying out a logarithmic compression of the extracted envelope and e) computing a propagation depth dependent attenuation coefficient of the tissues crossed by the ultrasound pulse in the target body as the slope of the line fitting the logarithmic compressed envelope data along the penetration depth of the ultrasound pulse in the target body. The disclosure relates also to an ultrasound system for carrying out the method.