Ventricular fibrillation (VF) is a life-threatening electromechanical dysfunction of the heart associatedtextlessbrtextgreaterwith complex spatiotemporal dynamics of electrical excitation and mechanical contraction of the hearttextlessbrtextgreatermuscle. It has been hypothesized that VF is driven by three-dimensional rotating electrical scroll waves,textlessbrtextgreaterwhich can be characterized by filamentlike electrical phase singularities or vortex filaments, but visualizingtextlessbrtextgreatertheir dynamics has been a long-standing challenge. Recently, it was shown that rotating excitation wavestextlessbrtextgreaterduring VF are associated with rotating waves of mechanical deformation. Three-dimensional mechanicaltextlessbrtextgreaterscroll waves and mechanical filaments describing their rotational core regions were observed in thetextlessbrtextgreaterventricles by using high-resolution ultrasound. The findings suggest that the spatiotemporal organizationtextlessbrtextgreaterof cardiac fibrillation may be assessed from waves of mechanical deformation. However, the complextextlessbrtextgreaterrelationship between excitation and mechanical waves during VF is currently not understood. Here, wetextlessbrtextgreaterstudy the fundamental nature of mechanical phase singularities, their spatiotemporal organization, and theirtextlessbrtextgreaterrelation with electrical phase singularities. We demonstrate the existence of two fundamental types oftextlessbrtextgreatermechanical phase singularities: “paired singularities,” which are colocalized with electrical phasetextlessbrtextgreatersingularities, and “unpaired singularities,” which can form independently. We show that the unpairedtextlessbrtextgreatersingularities emerge due to the anisotropy of the active force field, generated by fiber anisotropy in cardiactextlessbrtextgreatertissue, and the nonlocality of elastic interactions, which jointly induce strong spatiotemporal inhomogeneities in the strain fields. The inhomogeneities lead to the breakup of deformation waves and createtextlessbrtextgreatermechanical phase singularities, even in the absence of electrical singularities, which are typically associatedtextlessbrtextgreaterwith excitation wave break. We exploit these insights to develop an approach to discriminate paired andtextlessbrtextgreaterunpaired mechanical phase singularities, which could potentially be used to locate electrical rotor corestextlessbrtextgreaterfrom a mechanical measurement. Our findings provide a fundamental understanding of the complextextlessbrtextgreaterspatiotemporal organization of electromechanical waves in the heart and a theoretical basis for the analysistextlessbrtextgreaterof high-resolution ultrasound data for the three-dimensional mapping of heart rhythm disorders.