On-orbit periodic thermal loads degrade the reflector surface accuracy of AstroMesh antennas. To address this problem, a surface shape stability design method is proposed to passively pre-control the on-orbit thermal deformation of mesh reflectors, in which the structural parameters are properly designed to make the internal forces of the whole structure change coordinately and the surface shape of cable-mesh antennas insensitive to thermal loads. First, mathematical models of mechanical-thermal matching (MTM) are established for AstroMesh reflectors, in which an MTM model is developed for the cable net structure and the reflector membrane is equivalent to a cable net structure according to the force balance and thermal deformation coordination relationships. Then, based on the mathematical models, a surface shape stability design strategy is presented for AstroMesh antennas to properly design the cross-sectional dimensions of the cables. Finally, typical AstroMesh reflector structures are designed using the proposed method and simulation results show that the thermal deformations of the obtained AstroMesh reflectors are quite small under the whole temperature range. INDEX TERMS Mesh reflector antennas, thermal loads, surface shape stability, mechanical-thermal Matching (MTM).