The impulse response of the velocity potential and the discrete representation methods were used in order to model the acoustic field radiated by ultrasonic transducers and arrays. The first method deals with the calculation of the exact impulse response, in which solutions are possible only for simple geometries, such as the circular piston. The second method is an approximated solution based on the discretization of the acoustic aperture in small elementary areas, each of them radiating a spherical wave. By using circular transducers, which can be considered circular pistons, many simulations comparing the methods were carried out. The relation between the computational cost and the precision was analyzed, thus establishing the time and space discretization levels. The simulations were made using the Matlab software and the results were compared to experimental measurements showing good agreement. The experimental results were obtained using a scanning system. The acoustic field radiated from a 1 MHz circular transducer was measured as well as a 3.5 MHz array of 16 elements both immersed in water. The acoustic field radiated by the array was simulated and measured with focalization on a radius of 30 mm with deflections of 0º and 20º.