A thin circular structure, a string loop, vibrating in the central plane of a Schwarzschild black hole will be investigated. String loop stability and frequencies of its vibrational modes will be provided for different string equations of state. String are objects with tension and hence they can help us to understand the problem of relativistic elasticity; they can be also considered as simplified models for thin magnetic flux tubes from plasma physics. We used the vibrating string loop model to fit the quasi-periodic oscillation observed in X-ray signals coming from some compact sources.