In this research the transient flow analysis in viscoelastic pipes considering Fluid Structure Interaction have been performed utilizing a newly developed formulation of Transfer Matrix Method in frequency domain. To obtain this extended form of TMM, mathematical processes was accomplished. Time domain governing equations have been transformed to frequency domain and then a suitable matrix form of them is used to study transient flow due to sudden valve closure. Obtaining a set of algebraic equations instead of integral equations and the ability to analyze this phenomenon without need to solve complex convolution integral, are some of the benefits of the frequency domain tools, which have been applied in this research. To verify the model, initially two cases of rigid and elastic pipe wall have been analyzed. Results showed good conformity comparing to experimental data and analytical solution available. Then having a set of reliable experimental data of transient flow in VE pipe, MatLab code was adopted to the model and fortunately here also results were in good compatibility with the experimental results. Also it has been showed that this model will be a suitable tool for parametric analysis and for determining the critical situations of the system. The results obtained from this research prove that using frequency domain tools will lead to an effective and precise model for simulating the transient flow characteristics in VE and also normal transmitting pipelines.