Dynamic load in tubes due to detonation has plenty of applications such as the oil pipeline system and pulse detonation engine. Various experimental, analytical, and numerical investigations have been made to study the elastic-dynamic behaviors of tubes under internal moving pressure, with few studies dedicated to elastic-plastic analysis of this kind of problem. The investigation of elastic-plastic response of a tube made of homogeneous and nonhomogeneous (functionally graded material-FGM) materials subjected to the internal moving pressure (gaseous detonation) is the specific objective of this study. FGM is a newly well-established type of composite materials that its material contents are varying gradually along a user-defined direction. In this work, the effect of non-homogeneity on the vibrational response of the tube was studied using an axisymmetric FE model, which developed by Abaqus ® commercial package accompanied by VUMAT, VDLOAD, and VUSDFLD user-written subroutines. Different detonation load velocities were considered based on the tube material properties, i.e., according to the critical velocities. The presented results showed that the variation of stress/strain fields against time was affected by the gradation of FGM material. In addition, FGM material can help to withstand against the detonation loads, specifically when there are multiple sequential detonations or a high-pressure detonation load.