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The objective of this work is to study the dynamic behavior of FG pipe conveying fluid lying on the visco-elastic foundation using differential quadrature method. The material properties change constantly across the pipes thickness and depend on power law distribution. The vibration equations for FG pipe are obtained by using Hamilton's principle based on the Euler- Bernoulli model with (Clamped-Free) boundary conditions. An efficient numerical method by differential quadrature (GDQ) is developed to find the natural frequencies and stability for FG pipe. The effects gradient index and foundation parameters in fluid conveying FG pipes with certain flow velocity on frequencies are investigated. The present method of solution is accurately checked by comparing their results for fluid conveying pipe with the available results in the literature. From the comparison, a reasonable agreement was found. An increase in the gradient index results in an increase in the critical velocities for FG pipe.

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