The channels may be formed in the unconsolidated sands reservoir due to formation failure during high-pressure water injection or frac-packing. Based on the continuum mechanics, a mathematical model has been established to simulate the formation process of big channels in unconsolidated sands reservoir during fluid injection. The model considers the effect of reservoir heterogeneity, solid particles erosion, and deposition. The dynamic formation process of channels around the borehole and its influencing factors are analyzed by this model. The results indicate that the seepage erosion plays a very significant role in the formation of the channels during fluid injection for the unconsolidated sands with extremely low strength. The formation of the channels is closely related to the duration of fluid injection, injection pressure, reservoir heterogeneity, formation plugging, and critical fluid velocity. The long channels are more likely to form as injection time increases. Higher injection pressure will lead to higher flow rate, thus eroding the solid particles and forming big channels. The increase of the rock strength will enhance the value of critical fluid velocity, which makes it difficult for the occurrence of erosional channelization. The near-wellbore damage of the formation will decrease the flow rate, and the preferential flow channels are less likely to be induced under the same injection pressure when compared with undamaged formation. In addition, we also found that the reservoir heterogeneity is essential to the formation of preferential flow channels. The channels are especially prone to be formed in the regions with high porosity and permeability at the initial time. The study can provide a theoretical reference for the optimal design of high-pressure water injection or frac-packing operation in the unconsolidated sands reservoir.