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In this paper, using modified couple stress theory, dynamic stability of a cantilevered micro-tube embedded in several types of elastic media is studied. The governing equation for lateral vibrations of the micro-tube conveying fluid is derived using the extended Hamilton's principle. The numerical results are obtained by employing the extended Galerkin's method. For validation purposes, the obtained results for simple cases are compared and findings indicate a very good agreement with those available in the literature. The stability maps of different configurations with different flow velocities are studied and the influences of various parameters such as material length scale, external diameter and different elastic properties on the stability of the system are considered. Results indicate that elastic environments may enlarge the stability regions significantly at larger values of mass ratio parameter while decrease it for smaller values of mass ratio parameter. Moreover, using elastic media mathematically defined by series functions provides the capability to simulate almost any real time operational environment the micro-tube embedded in and results in an optimal stability state of the micro-structure carrying fluid flow.

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