In this paper the principle of energy balance approach is applied to develop a swallowtail catastrophe model for transient stability analysis of a multimachine power system. A new swallowtail catastrophe manifold function equation is created with the help of a simple energy balance equation of the critical machine in the interconnected multimachine power system, which is the sum of its transient kinetic energy during the fault-on period and the potential energy of the post fault period. The bifurcation set of the swallowtail catastrophe gives the transient stability region of the power system, and the critical fault clearing time is computed from the swallowtail catastrophe manifold function equation. The computer simulation on a three-machine power system is presented, and the simulation results are compared with the standard step-by-step numerical method of integration. The method appears to be a promising technique for on-line transient stability assessment of multimachine power systems.