The influence of the extra dimensions on the equilibrium and radial pulsation of a compact object is investigated. For such purpose, we solve the stellar structure equations and radial pulsation equations, both modified from their original version to include the extra dimensions (d ≥ 4) taking into account that spacetime outside the object is depicted by a Schwarzschild-Tangherlini metric. In addition, we consider that the pressure and the energy density are connected by a linear relation. Some properties of compact objects are analyzed, such as mass and period of the fundamental mode and their dependencies with the spacetime dimensions. We found that the maximum mass marks the begining of the instability, indicating that in a sequence of equilibrium configurations, the regions constitute by stable and unstable compact objects are distinguished by the relations and, respectively.