This study focuses on the dynamic behavior of a cantilevered fluid conveying hybrid pipe (FCHP) consisting of two different materials (aluminum and steel), and resting on a two-parameter elastic soil. To analyze the fluid-structure interaction in a hybrid pipeline conveying fluid, the pipe was modeled as an Euler-Bernoulli beam, and the equation of motion that describes the behavior of the dynamics of the Euler-Bernoulli beam was obtained. The critical velocities and complex frequencies of the system were obtained by utilizing the differential transformation method (DTM). Although studies on pipes supported on two-parameter elastic soil and FCHPs consisting of two different materials have been conducted separately by several researchers, a detailed study investigating the behavior of these two systems together has not been published so far. The stability of such a system is affected by various parameters. Therefore, in this study, the effects of the two-parameter elastic soil, the length ratio of the hybrid pipe materials, and the soil types and properties on the dynamic instability of a FCHP were investigated in detail. The results of this study showed that the critical flow velocity increased with the existence of a two-parameter elastic soil; the critical flow velocity of the FCHP increased with increasing foundation and shear modulus values; although the length ratio affected the instability of the cantilevered FCHP with and without elastic foundation, the FCHP resting on stiff clay foundation was more affected by this parameter in comparison to the FCHP resting on dense sand foundation having higher foundation and shear modulus values; and the critical flow velocity curves contained S and Z shaped segments associated with the instability-restabilization-instability sequence of the system.