The evaluation of cardiac anisotropic mechanics is important in the diagnosis of heart disease. However, other representative ultrasound imaging-based metrics, which are capable of quantitatively evaluating anisotropic cardiac mechanics, are insufficient for accurately diagnosing heart disease due to the influence of viscosity and geometry of cardiac tissues. In this study, we propose a new ultrasound imaging-based metric, maximum cosine similarity (MaxCosim), for quantifying anisotropic mechanics of cardiac tissues by evaluating the periodicity of the transverse wave speeds depending on the measurement directions using ultrasound imaging. We developed a high-frequency ultrasound-based directional transverse wave imaging system to measure the transverse wave speed in multiple directions. The ultrasound imaging-based metric was validated by performing experiments on 40 rats randomly assigned to four groups; three doxorubicin (DOX) treatment groups received 10, 15, or 20 mg/kg DOX, while the control group received 0.2 mL/kg saline. In each heart sample, the developed ultrasound imaging system allowed measuring transverse wave speeds in multiple directions, and the new metric was then calculated from 3-D ultrasound transverse wave images to evaluate the degree of anisotropic mechanics of the heart sample. The results of the metric were compared with histopathological changes for validation. A decrease in the MaxCosim value was observed in the DOX treatment groups, with the degree of decrease depending on the dose. These results are consistent with the histopathological features, suggesting that our ultrasound imaging-based metric can quantify the anisotropic mechanics of cardiac tissues and potentially be used for the early diagnosis of heart disease.