Mass conservation is an important factor in the construction of the general circulation model on the quasi-uniform overset spherical Yin-Yang grid, and is also a key issue when applying the Yin-Yang grid to numerical models. With the help of a flux-form advection equation, we carried out a series of idealized numerical tests on a sphere to assess three conservative constraints in addition to the non-conservative boundary interpolation scheme. The test cases included a standard solid-body advection, a benchmark deformational flow, and a sine-wave advection. The results showed that the conservative constraint of mass property is important for global numerical integration and has an effect on the computational accuracy. The global conservative constraint that ensures local mass conservation gave accurate results. The boundary flux identification based on cell-wise mass constant distribution on the Yin-Yang grid achieved local and global mass conservation without either decreasing the computational accuracy or increasing computing costs. This algorithm is computationally efficient and can be an effective numerical scheme for mass conservative constraints on the overset Yin-Yang grid. However, while the boundary flux identification based on cell-wise linear distribution can improve the computational accuracy, it requires much more calculation time, which will limit its application in a dynamical model.