A novel multistage numerical modeling approach to simulate acoustic‐wave generation and propagation of an electromagnetic acoustic transducer (EMAT) is presented. The model assumes a uniform static magnetic field in a conducting half‐space. A meander coil winding situated above the half‐space is driven by a transient high‐frequency current pulse. The numerically computed eddy currents in the conducting specimen are combined with the static magnetic field to yield spatially and temporally diffusive Lorentz forces which in turn are coupled into the elastic‐wave equation. This hyperbolic elastodynamic system is solved for the displacement field vector which gives rise to propagating elastic waves. Numerical transduction results are discussed for a generic two‐wire transient EMAT configuration and for an isotropic half‐space with electric and acoustic material parameters equivalent to those of aluminum.