This paper presents a boundary integral method for calculating the potential field generated by external stimulation at locations within the heart using realistic heart geometry and samples of the potential taken from the epicardial surface. This method assumes the heart is homogeneous and isotropic. To test the method we made epicardial and endocardial measurements in dogs during transthoracic pacing stimuli. From the epicardial potential measurements we predicted the endocardial potential values and compared them with the measured data. Despite the seemingly gross assumptions, the mean correlation coefficient between the measured and predicted potentials for three dogs and eleven stimulation electrode configurations was 0.985, and the mean rms error was 17%.