Abstract The propagation of pressure pulses of arbitrary time form in inhomogeneous attenuating media with characteristics similar to real biological tissues is considered. A mathematical model using the quasi-optical approximation is developed to solve the wave equation. Such a model proves to be convenient for computer realization. A spectral analysis of known experimental data on frequency dependent backscatter is realized to separate coherent and incoherent components of backscatter from tissues and determine their parameters. The characteristics of the scattering are utilized for digital simulations of ultrasound propagation from an interrogated tissue volume. The results presented describe the expected space distribution of the pressure amplitude and phase near the transducer focus in the presence of an aberrating layer with parameters characteristic of abdominal imaging.