The Luo Rudy phase I heart model is used in this paper to study the propagation of waves generated by point wave sources in one- and two-dimensional weakly coupled myocardial tissues. It is observed that the weak coupling can lead to the reduction of the wave propagation speed. When there is a large coupling intensity gradient in the myocardial tissue, weak coupling can lead to the frustration of wave propagation and early afterdepolarization showed by cardiomyocytes. When the coupling intensity between cardiomyocytes is low enough, circular motion of wave and complex wave propagation can be observed in myocardial tissues. In addition, we also study the propagation of planar wave in two-dimensional weakly coupled myocardial tissues by constructing two different two-dimensional myocardial tissues with different coupling structures. We find that spiral waves can be spontaneously generated when plane wave propagates in the two myocardial tissues. Increasing the coupling intensity between cells can effectively prevent the circus movement of wave and the spontaneous generation of spiral wave. The physical mechanism of the above phenomenon is analyzed in this paper.