3D ultrasound imaging has high potential for various clinical applications, but often suffers from high operator-dependency and the directionality of the acquired data. State-of-the-art systems mostly perform compounding of the image data prior to further processing and visualization, resulting in 3D volumes of scalar intensities. This work presents computational sonography as a novel concept to represent 3D ultrasound as tensor instead of scalar fields, mapping a full and arbitrary 3D acquisition to the reconstructed data. The proposed representation compactly preserves significantly more information about the anatomy-specific and direction-depend acquisition, facilitating both targeted data processing and improved visualization. We show the potential of this paradigm on ultrasound phantom data as well as on clinically acquired data for acquisitions of the femoral, brachial and antebrachial bone.