The objectives were to develop a novel three-dimensional technology for imaging naturally occurring shear wave (SW) propagation, demonstrate feasibility on human volunteers and quantify SW velocity in different propagation directions. Imaging of natural SWs generated by valve closures has emerged to obtain a direct measurement of cardiac stiffness. Recently, natural SW velocity was assessed in two dimensions on parasternal long axis view under the assumption of a propagation direction along the septum. However, in this approach the source localization and the complex three-dimensional propagation wave path was neglected making the speed estimation unreliable. High volume rate transthoracic acquisitions of the human left ventricle (1100 volume/s) was performed with a 4D ultrafast echocardiographic scanner. Four-dimensional tissue velocity cineloops enabled visualization of aortic and mitral valve closure waves. Energy and time of flight mapping allowed propagation path visualization and source localization, respectively. Velocities were quantified along different directions. Aortic and mitral valve closure SW velocities were assessed for the three volunteers with low standard deviation. Anisotropic propagation was also found suggesting the necessity of using a three-dimensional imaging approach. Different velocities were estimated for the three directions for the aortic (3.4$pm$0.1 m/s, 3.5$pm$0.3 m/s, 5.4$pm$0.7 m/s) and the mitral (2.8$pm$0.5 m/s, 2.9$pm$0.3 m/s, 4.6$pm$0.7 m/s) valve SWs. 4D ultrafast ultrasound alleviates the limitations of 2D ultrafast ultrasound for cardiac SW imaging based on natural SW propagations and enables a comprehensive measurement of cardiac stiffness. This technique could provide stiffness mapping of the left ventricle.