Potential inverse electrocardiography (PIE) is a method for reconstruction of epicardial potentials from measured body surface electrocardiograms and heart-torso geometry. The method of choice for computing epicardial potentials has been either the boundary element method (BEM) or the finite element method (FEM). These methods require time-consuming meshing of the heart and torso surfaces or the volume between the two surfaces. Moreover, meshing can introduce artifacts in the reconstructed epicardial images if optimization is not carefully done. Here we introduce the application of a meshless method, the method of fundamental solutions (MFS) to PIE in the hope of overcoming such meshing-related problems. This study shows that MFS is a promising meshless alternative to BEM and FEM in PIE.