A low-frequency, omni-directional A0 Lamb wave ElectroMagnetic Acoustic Transducer (EMAT) is developed for applications in guided wave tomography, operating at 50 kHz on a 10 mm thick steel plate. The key objective is to excite an acceptably pure A0 wave mode in relation to the S0 mode, which can also be present at this operating point and is desired to be suppressed by approximately 30 dB. For that, a parametric Finite Element (FE) model of the design concept is implemented in a commercially available FE software, where the bias magnetic field is calculated initially, then combined with the eddy current caused by the induction coil to produce a force. A numerical optimization process employing a genetic algorithm is set up and the EMAT design is optimized to yield an improved A0 mode selectivity. The parameters subjected to optimization are the magnet diameter and the magnet lift-off, which control the direction of the exciting force in the skin depth layer and therefore the mode selectivity. Although there are three possible electromagnetic acoustic interaction mechanisms, the optimisation considers only the Lorentz force, as its performance surface contains a clear optimum and from the optimised design a physical prototype is built. The FE model is validated against measurements on an aluminium plate for the Lorentz force excitation mechanism and on a steel plate for both the Lorentz and magnetisation force. For the steel plate, it is found that only considering the Lorentz force leads to a significant overestimation of the mode selectivity, as the S0 amplitude is underestimated by the Lorentz force, but the A0 amplitude remains mainly uninfluenced. Further, it has been found that additionally including the magnetisation force into the optimisation leads to a better mode selectivity, however, the optimisation drives the optimum to a minimum magnet diameter and therefore reduces the EMAT sensitivity. In a numerical study robustness is shown for fairly large variations of the magnet lift-off and the magnetic permeability. Based on the findings, a two-step model-based design approach is proposed whereby only the Lorentz force is used in the first step for the optimisation and then in a second step, a realistic estimate of the mode selectivity of the optimised design can be obtained by additionally considering the magnetisation force.