Based on strain gradient theory, a microstructure-dependent Timoshenko beam model is pre- sented, for the first time, to analyze the vibration and structural instability of the micro scale pipes conveying fluid. The governing equations are derived using Hamilton principle. This new model contains three material length scale parameters which interpret the size effect. The present model reduces to the modified couple stress model and the classical model when two and all of these three material length scale parameters become zero, respectively. Then, the differential quadrature method is applied to solve the equations of motion. Finally, the ef- fects of the material length scale parameters and Poisson ratio on the vibrational characteris- tics and stability are explored. It is found that the natural frequencies and the critical flow ve- locities predicted by the present strain gradient model are higher than those predicted by the modified couple stress model and the classical model. Specially, when the outside diameter of the micropipe is comparable with the material length scale parameter, the size effect is significant. Moreover, the Poisson effect on the critical flow velocities shows an extreme point phenomenon for the two non-classical models, which is quite different from that pre- dicted by the classical model.

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