The marine risers are generally used as the main transport means for economic materials and resources discovered undersea. In general, the marine risers are secured at either an offshore platform or a vessel. Both ends of the riser are to be adjusted to obey with the design criteria but in many cases their rotational stiffness is hardly set free for the hinge connection. This paper integrates the analytical investigation and the design consideration for the effects of end supports on the free vibrations of a marine riser conveying fluid. It is well known that resonances of marine risers/pipes can cause excessive stress and strain responses, leading to ultimate fatigue failure of the riser system. To avoid a resonance resulting in the sustainable use of the riser, the study to evaluate the influence of end rotational stiffness on the natural frequency of a marine riser conveying fluid is imperative. Using variational principle, the riser model formulation includes both the bending rigidity and the axial elasticity. Using Galerkin finite element method, the natural frequencies and their corresponding mode shapes are determined. The highlight in this paper is the free vibration behaviours in the transition from hinge to fully fixed ends, which can indicate a health monitoring methodology of the risers. The design concepts for the marine risers/pipes conveying fluid to minimize the influence of support conditions are discussed herein as a guideline for structural offshore engineers.