In the present work, structural joints have been modeled as a pair of translational and rotational springs and frequency equation of the overall system has been developed using sub-structure synthesis. It is shown that using first few natural frequencies of the system, one can obtain a set of over-determined system of equations involving the unknown stiffness parameters. Method of multi-linear regression is then applied to obtain the best estimate of the unknown stiffness parameters. The estimation procedure has been developed first for a two parameter joint model and then for a three parameter model, in which cross coupling terms are also included. Two cases of structural connections have been considered, first with a cantilever beam with support flexibility and then a pair of beams connected through lap joint. The validity of the proposed method is demonstrated through numerical simulation and by experimentation.