Sonoporation mediated by microbubbles is being extensively studied as a promising technology to facilitate gene/drug delivery to cells. However, the theoretical study regarding the mechanisms involved in sonoporation is still in its infancy. Microstreaming generated by pulsating microbubble near the cell membrane is regarded as one of the most important mechanisms in the sonoporation process. Here, based on an encapsulated microbubble dynamic model with considering nonlinear rheological effects of both shell elasticity and viscosity, the microstreaming velocity field and shear stress generated by an oscillating microbubble near the cell membrane are theoretically simulated. Some factors that might affect the behaviors of microstreaming are thoroughly investigated, including the distance between the bubble center and cell membrane (d), shell elasticity (χ), and shell viscosity (κ). The results show that (i) the presence of cell membrane can result in asymmetric microstreaming velocity field, while the constrained effect of the membrane wall decays with increasing the bubble-cell distance; (ii) the bubble resonance frequency increases with the increase in d and χ, and the decrease in κ, although it is more dominated by the variation of shell elasticity; and (iii) the maximal microstreaming shear stress on the cell membrane increases rapidly with reducing the d, χ, and κ. The results suggest that microbubbles with softer and less viscous shell materials might be preferred to achieve more efficient sonoporation outcomes, and it is better to have bubbles located in the immediate vicinity of the cell membrane.