An analytical model to study the coupled transverse and longitudinal vibrations of a single lap adhesive joint is proposed in this paper which includes partial differential form of the motion equations. A balanced single lap adhesive joint consist of two identical adherents of mild steel which are lap jointed over a certain length by a viscoelastic material,
epoxy resin(araldite). Adherents are modeled as Euler-Bernoulli Free-Free beam. Both transverse and axial deformation of adherents, shear and peel stresses at the adhesive joint interface and deflection of mid plane of adhesive layer (3-parameter model) is considered in deriving the equations of motion. The classical two parameter elastic foundation model violates the equilibrium condition of the adhesive layer; to eliminate this flaw, a new three parameter elastic foundation model is
considered which satisfies the equilibrium condition of the adhesive layer. The governing equations of motions are derived for three parameter elastic foundation model. The numerical solutions of the governing equations for free vibrations yield the system natural frequency. Experimentation carried out on both monolithic and adhesively jointed beam to observe the effect of joint. The effect of thickness of adhesive and joint overlap ratio on system natural frequencies are investigated.