In the last decades, the field of structural health monitoring and damage detection has been intensively explored. Active vibration techniques allow to excite structures at high frequency vibrations which are sensitive to small damage. Piezoelectric PZT transducers are perfect candidates for such testing due to their small size, low cost and large bandwidth. Current ultrasonic systems are based on external piezoelectric transducers which need to be placed on two faces of the concrete specimen. The limited accessibility of in-service structures makes such an arrangement often impractical. An alternative is to embed permanently low-cost transducers inside the structure. Such types of transducers have been applied successfully for the in-situ estimation of the P-wave velocity in fresh concrete, and for crack monitoring. Up to now, the design of such transducers was essentially based on trial and error, or in a few cases, on the limitation of the acoustic impedance mismatch between the PZT and concrete. In the present study, we explore the working principles of embedded piezoelectric transducers which are found to be significantly different from external transducers. One of the major challenges concerning embedded transducers is to produce very low cost transducers. We show that a practical way to achieve this imperative is to consider the radial mode of actuation of bulk PZT elements. This is done by developing a simple finite element model of a piezoelectric transducer embedded in an infinite medium. The model is coupled with a multi-objective genetic algorithm which is used to design specific ultrasonic embedded transducers both for hard and fresh concrete monitoring. The results show the efficiency of the approach and a few designs are proposed which are optimal for hard concrete, fresh concrete, or both, in a given frequency band of interest.