Abstract: The acoustic nonlinearity parameter, B/A, is a fundamental material constant characterizing nonlinear properties of biological media. Knowledge of the B/A of biological fluids or soft tissues through which pulsed acoustic waves generated from clinically relevant probes are propagating is necessary whenever high intensity pressure fields are produced. The numerical model recently developed in our lab, capable of predicting the pulsed sound fields generated from axisymmetric sources in nonlinear attenuating media, was a powerful instrument for investigating nonlinear acoustic fields produced from circular plane or focused sources in attenuating media in dependence on boundary condition parameters. Quantitative analysis of the obtained results enabled developing the alternative method for determination of the B/A parameter of biological media. First, the method involves measuring in the near field of a piezoelectric transducer the nonlinear waveform distortion of the pulsed acoustic wave propagating through the two-layer system of media: water-tested material. Then, the method involves numerical modeling, in frequency domain and under experimental boundary conditions, the nonlinear waveform distortion of the propagating wave by using the Time-Averaged Wave Envelope (TAWE) approach [1]. The obtained numerical simulation results were fitted to the experimental data by adjusting the B/A parameter of the tested material. The determined values of the B/A for standard media considered (corn oil, glycerol, pig blood, homogenized pig liver), whose density, sound velocity and attenuation law have been preliminary determined experimentally, are in a good agreement with those published. The proposed method ensure the decimal degree of accuracy, is relatively simple to use and requires small volume of tested materials that is important because of difficulty of their availability.