Based on the coupled acoustic scattering of two neighboring fluid-filled thin elastic shells suspending in an unbounded viscous liquid, an analytical method is developed to calculate the acoustic radiation force (ARF) of the shells. Two physical effects are taken into account: elastic radiation scattering and the multiple interactions of shells. Numerical results reveal that the magnitude of ARF can be enhanced by the sound radiation from the elastic shell undergoing forced vibrations and two resonant peaks can be observed on the ARF function curves. The feature of the lower peak is determined by the interactions and acoustic response of the back shell. The attractive forces can be obtained in the low kR1 band for the case of radius ratio R2/R1 > 1, while the magnitude of ARF at the lower peak may be influenced to some extent by acoustic shielding phenomenon for the case of radius ratio R2/R1 < 1. Accordingly, the interactions of particles cannot be ignored. The results may provide a theoretical basis for precisive manipulation of multiple particle systems.