<p>Hydrogen gas flowing through pipes permeates through the pipe wall and induces compressive stress within the pipe material. This phenomenon, together with hydrogen embrittlement, reduces the pipe strength. This article examined the flow-induced buckling vibration response of a functionally graded pipe conveying hydrogen gas on a Pasternak foundation. The hydrogenation stress in the pipe material was derived by modifying Stashchuk and Dorosh's hydrogen stress model of a cylindrical metal block. The dynamic model of the hydrogen conveying pipe was developed using the Reddy–Bickford third-order beam theory, incorporating the hydrogenation stress. A comparison study was undertaken, and the results indicate that the present derivation is consistent with the model based on Timoshenko theory when a small-bore, thin-walled pipeline is considered. However, further comparison using a large-bore, thick-wall pipeline, the present model predicts higher values of the critical velocity and the initial compression. This study also examines the effect of hydrogenation, temperature, and Pasternak parameter on the buckling characteristics of the pipelines. The results show that hydrogenation and thermal load lower the pipeline's resistance to buckling. Also, hydrogen pressure and fluid velocity raised the likelihood of buckling in the pipe. Comparing the buckling of FGM and steel, the values of the critical buckling parameters were observed to be higher in FGM than in steel. The presence of ceramics reduces the chances of buckling in the FGM pipe.</p>