As an attempt to further improve the reliability and effectiveness of ultrasonic testing (UT), a two-dimensional numerical simulator of UT was developed. The simulator models the wave medium (or test object) using the mass-spring lattice model (MSLM) that consists of mass-points and springs. Some previous simulation results, obtained by using MSLM, are briefly reviewed in this paper, for propagation, reflection, and scattering of ultrasonic waves. Next, the models of transmitting and receiving piezoelectric transducers are introduced with some numerical results, which is a main focus of this paper. The UT simulator, established by combining the transducer models with the MSLM, was used to simulate many UT setups. In this paper, two simple setups are considered as examples, and their simulated A-scan signals are discussed. The potential of the MSLM, transducer models, and the UT simulator developed in this study to be used in the actual UT is confirmed.