Abstract: The previous dynamic flexibility (DF) method andimproved DF method for extracting constrained structural modes froma free test are only suitable to structures with rigid supports.However elastic supports are widely used in engineering structures. For thisreason, a general method for extracting modes of constrained structureswith elastic supports from a free test is developed here. It is called ageneral method because: (i) When the stiffness of the supports is verylarge, the method gives modes of a constrained structure withrigid supports; (ii) When the stiffness of the supports is quite small,free-free modes can obtained, in which the structure is suspended byusing rubber ropes etc; (iii) When the stiffness of the supports isarbitrary, the method can give satisfactory results.These show that the algorithm propsed in this paper has a wideapplication in engineering.