The attenuating properties of biological tissue are of great importance in ultrasonic medical imaging. Investigations performed in vitro and in vivo showed the correlation between pathological changes in the tissue and variation of the attenuation coefficient. In order to estimate the attenuation we have used the downshift of mean frequency (fm) of the interrogating ultrasonic pulse propagating in the medium. To determine the fm along the propagation path we have applied the fm estimator (I/Q algorithm adopted from the Doppler mean frequency estimation technique). The mean-frequency shift trend was calculated using Single Spectrum Analysis. Next, the trends were converted into attenuation coefficient distributions and finally the parametric images were computed. The RF data were collected in simulations and experiments applying the synthetic aperture (SA) transmit-receiving scheme. In measurements the ultrasonic scanner enabling a full control of the transmission and reception was used. The resolution and accuracy of the method was verified using tissue mimicking phantom with uniform echogenicity but varying attenuation coefficient.