This paper is concerned with a mathematical modeling of ultrasonic excitation signal generated by electromagnetic acoustic transducer (EMAT). Target inspection service is assumed to be directed to ferromagnetic materials. The set of impact models by EMAT are then described by a static magnetic problem, an eddy current problem, and a magnetic-elastic coupling problem. First, the bias magnetic field by permanent magnets can be described by a nonlinear static magnetic field model. Secondly, the dynamic magnetic field by electrical coil can be analyzed by a time-dependent linear electro-magnetic model. Thirdly, the magnetic-elastic coupling is generated by interaction between bias and dynamic magnetic fields. Finally impact models of ultrasonic test signals are formulated as total effects by Lorentz, magnetization, and magnetostrictive forces. Some control issues related to nondestructive evaluation are also discussed under our framework.