The propagation of diagnostic ultrasonic imaging pulses in tissue and their interaction with contrast microbubbles is a complex physical process. Our model driven approach is used to gain better knowledge of the different processes involved in the generation of the backscattered contrast echo. It can be divided into three separable stages: linear and nonlinear wave propagation in tissue, the resulting echo from the pulse interaction with the contrast microbubble, and the propagation of the scattered echo. A simplified approach of field simulation is chosen due to the complexity of the task and necessity to estimate comparative contributions of each component of the process. A modified method for spatial superposition of attenuated waves was further developed to enable simulations of low intensity pulse fields in nonlinear attenuating and liquid-like biological medium using weakly focused transducers. Simulations of the acoustic bubble response are carried out with Rayleigh-Plesset equation with the addition of the radiation damping. Theoretical simulations show that contrast bubbles interaction with excitation pulses is the main cause of nonlinear distortions, and a 2-3 dB increase of second harmonic amplitude depends on nonlinear distortions of incident pulse.