The subject of this study is shear stress exerted on the cell membrane by acoustic microstreaming generated by a contrast microbubble pulsating nearby a cell. This effect is presumed to play a major role in the sonoporation process. Currently, the existing model of this effect is based on an equation that has been derived for a free hemispherical bubble resting on a rigid plane. Such a model is not adequate for an encapsulated bubble such as a contrast agent microbubble. In this study, an improved theory is suggested that assumes an encapsulated bubble to be detached from the cell membrane. The new model allows one to calculate the shear stress distribution on the cell membrane and to determine the position and the magnitude of the peak shear stress at different values of the acoustic parameters. The second problem under consideration is how to apply the model for pairwise bubble-cell interactions to bubble-cell solutions which one has to deal with in experiments. An approach is proposed to evaluate the number of cells undergoing sonoporation in a bubble-cell solution. It is shown that the reaction of a bubble-cell solution to the variation of the acoustic parameters can be different from what is expected from the analysis of pairwise interactions between single bubbles and cells. In particular, the attenuation of the driving acoustic wave caused by bubbles can considerably reduce the total efficiency of sonoporation in the solution at frequencies close to the resonance frequency of bubbles of dominant size. Numerical examples for a polydisperse bubble population are presented.