The mechanism of solute transport around the wellbore was found to play an important role in the single-well push-pull (SWPP) test, but it was grossly overlooked in previous studies. For instance, the mixing effect of injected tracer with water in the wellbore was ignored in analyzing both injection and extraction phases of SWPP. In this study, new models were developed by including such a mixing effect in the wellbore. Two types of boundary conditions at the wellbore were considered: the resident concentration continuity (RCC) and the flux concentration continuity (FCC). To test the assumptions used in the mathematical model, the stochastic modeling, the numerical simulation and the laboratory-controlled experiment were executed. Results showed that the SWPP test was sensitive to the mixing effect in both injection and extraction phases. A larger wellbore volume could result in a smaller concentration at the late stage of the extraction phase. FCC was more reasonable in describing solute transport at the wellbore-aquifer interface than RCC, and the difference between them decreased with decreasing radial dispersivity. The MODFLOW/MT3DMS package contained an invalid assumption on the mixing effect for the SWPP test. Stochastic modeling demonstrated that the homogeneous assumption was a good approximation for the reality when the variance of natural logarithm of the auto-correlated hydraulic conductivity field was less than 0.25 (σ_lnK^2≤0.25). The laboratory-controlled experiment showed that the radial ADE model of this study worked well for the well-sorted sand aquifer.