We construct a gravitational superconducting model composed of gravitationa
l London equations, gravitational Meissner and shielding effects, a gravita
tional fluxoid, and oscillation modes of a particle beam in a thin cylindri
cal gravitational superconductor. This model is applied to the study of neu
tron stars. An experiment to check the gravitational shielding in a terrest
rial laboratory using the Supertrons of Matsuzawa is proposed as well.