Recent developments in materials and cost reduction have led the study of the vibrational stability of pipelines conveying fluid to be an important issue. Nowadays, this analysis is done both by means of simulation with specialized softwares and by laboratory testing of the preferred materials. The former usually requires of complex modelling of the pipeline and the internal fluid to determine if the material will ensure vibrational stability; and in the latter case, each time there is a mistake on the material selection is necessary to restart all the process making this option expensive. In this paper, the classical mathematical description of the dynamic behavior of a clamped-pinned pipeline conveying fluid is presented. Then, they are approximated to a Hamiltonian system through Garlekin’s method being modelled as a simple linear system. The system stability has been studied by means of the eigenvalues of the linear system. From this analysis, characteristic expressions dependent on material constants has been developed as inequalities, which ensures the stability of the material if it matches all expressions. This new model provides a simplified dynamical approximation of the pipeline conveying fluid depending on material and fluid constants that is useful to determine if it is stable or not. It is worth to determine that the model dynamics does not correspond with the real, but the global behaviour is well represented. Finally, some simulations of specific materials have been use to validate the results obtained from the Hamiltonian model and a more complex model done with finite element software.