Longitudinal and transverse plane waves were simulated in a two-dimensional model of the myocardium. Their interactions with barriers were studied. The mechanisms for conduction delay, conduction facilitation, and block received special attention. It is shown that for a funnel-like structure the critical opening for propagation to occur depends on the anisotropy ratio and the longitudinal and transverse length constants. A mechanism which converts the block to propagation through tortuocity by conveniently placing barriers was demonstrated for both longitudinal and transverse plane waves. It is shown that the myocardium is a very robust structure, since the plane wave recovers quickly after the delay regions.