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In this paper, the various methods of estimating the attenuation and velocity of ultrasound in biological media are described. Special attention is paid to the influence of the transducer used in the measurement, i.e., the diffraction effect. This influence is investigated in a systematic way using realistic three-dimensional computer simulation techniques. The results of the analysis are given as universal sets of curves. These curves can be used by the interested reader to estimate the influence of the diffraction effect on the measurements for his own experimental conditions. Methods of preventing the systematic errors caused by the diffraction effect are discussed. For the sake of completeness, the effect of velocity dispersion on the measurement of velocity in tissues is discussed as well.