The one-dimensional unsteady flow equations for flow in an elastic tube have been solved by employing the method of characteristics and used to predict the development of the flow and pressure wave forms in the left coronary artery system of the horse. Input data to this model include in vivo measurements of wave speed and aortic-root pressure, both of which were carried out in horse experiments. In addition, estimates of vessel taper and fluid losses due to branching were established from plastic casts of the horse coronary arteries and from in vivo flowmeter data. The calculated results have confirmed earlier experiments in revealing a relatively large systolic component of flow in the major epicardial vessels. However, the calculations indicate that, once within the myocardium, the systolic flow component quickly diminishes and the diastolic flow component becomes increasingly important. The pressure pulse does not peak as observed in the aorta, but rather rounds out with systolic pressures decreasing slowly and diastolic pressures decreasing more rapidly with distance from the coronary ostium. The presence of relatively large amplitude, low frequency waves (of the order of 5–10 Hz), which were observed mainly during diastole in horse experiments, has also been confirmed by the computer calculations. Similar calculations carried out for conditions simulating the dog and human coronary systems indicate that such oscillations become higher in frequency and lower in amplitude with decreasing animal size.