The dynamics of mesh reflectors are characterized by large deformation when antennas undergo a large motion in the deployment process. In this work, absolute node coordinate formulation (ANCF), with the merit of precise description of large deformation, is employed to consider the flexibility of the reflector net. From a practical perspective, the effect of the torsional spring is incorporated into the dynamic governing equations by an equivalent mechanical model. Deployment simulation of the mesh reflector antennas is performed by a numerical procedure. It can be found that with the action of a degenerative driven force caused by the friction effect, the deployed process of antennas exhibits a character of asynchronous deployment. Additionally, a significant increase in tension during the final period of deployment has an intense influence on smooth deployment.