Echocardiography requires imaging of the heart with sound propagating at varying angles relative to the predominant direction of the myofibers. The degree of anisotropy of attenuation can significantly influence ultrasonic imaging and tissue characterization measurements in vivo. This study quantifies the anisotropy of attenuation of freshly excised myocardium at frequencies typical of echocardiographic imaging. Results show a significantly larger anisotropy than previously reported in specimens of locally unidirectional myofibers. Through-transmission radio frequency-based measurements were performed on specimens from 12 ovine and 12 bovine hearts. Although ovine hearts are closer in size to human, the larger size of bovine hearts offers the potential for specimens in which myofibers are more nearly unidirectionally aligned. The attenuation coefficient increased approximately linearly with frequency. The mean slope of attenuation with frequency was 3-4 times larger for propagation parallel than for perpendicular to the myofibers. At perpendicular insonification, slopes between ovine and bovine myocardium were approximately equal. However, attenuation in bovine specimens was larger for angles approaching parallel. The difference in results for parallel appears consistent with what might be expected from increased myofiber curvature associated with smaller lamb hearts. Quantitative knowledge of anisotropy of attenuation may be useful in understanding mechanisms underlying the interaction of ultrasound with myocardium.