The transient stability problem has grown to enormous size due to the large number of interconnections of power systems . As the problem size has grown, so has the computational effort and time required for solution . This paper introduces a powerful but simple matrix method for digital computer manipulation of the set of differential and algebraic equations which describes the power system . The system equations have the normal state-space form . Representation of the voltage control and the speed governor is included in the mathematical model of each machine in the system . Computer results on a multimachine power system are presented .