Operational spacecraft are facing a risk of collision with space debris objects. The net capturing method has been proposed to mitigate this risk on spacecraft. The mass-spring model is usually applied for net modeling by discretizing a cable into one or several mass-spring-damper elements in simulation. The absolute nodal coordinates formulation (ANCF) has also been applied to model the net, and this model is able to describe the flexibility of a net using less elements. However, the influence on the net behavior in simulation by the flexibility modeling of a net is not well understood and barely discussed. In this paper, flexibility models of a net are established based on the mass-spring model and the ANCF model,respectively. The influence on the net behavior by the flexibility modeling is, for the first time, analyzed via simulations. Two case studies of capturing a ball and a cube shaped targets are performed. It is found that the flexibility modeling has little influence on the net dynamics in simulation. Finally, the characteristics and benefits of the ANCF model are described and analyzed. A drawback of the ANCF model was found to be its inferior computational performance.