The paper studies analytically the free vibration of a generalised suspension system. The system is composed of a rigid body with thesymmetric shape about its centroid and two symmetrically inclined massless strings with infinite axial stiffness. The two hanging pointshave horizontal and vertical elastic supports. The rigid body is eccentrically acted by horizontal, vertical and rotational springs. A typicalapplication of the model is to represent a section of cable suspended bridges involving the lateral vibration of small amplitude. Thegoverning differential equations with three degrees-of-freedom are derived where the effect of gravitational potential is considered. Thestatic equilibrium position is determined simultaneously. When the elastic constraints are applied at the centroid of the rigid body,the vibration modes of the system can be divided into symmetric and antisymmetric ones which are studied independently. The analyticalexpressions of natural frequencies for some special cases are also provided. The effects of various parameters, especially the length andinclined angle of the strings, on the natural frequencies of the system are examined. Some useful conclusions are obtained. Simple modeldemonstration and verification are conducted to verify some findings in the paper.