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We have developed a three-dimensional ultrasound computer tomography system (3D USCT) for early breast cancer diagnosis. The method gives reproducible volume images of the female breast in 3D. The optimized aperture and transducer array systems show at the used low ultrasound frequency of 2.5 MHz a very high image quality. In contrast to other methods our system has a nearly isotropic and spatially invariant 3D point spread function (PSF) with a resolution of 240 11m as measured with a 70 11m AI bond wire. By simulated spectra including the experimentally measured noise of transmission tomography it could be shown that structures down to 4 mm could be reconstructed in speed of sound images. The reconstruction of the 3D images in reflection tomography could be accelerated by the use of the multi-core structure of PCs and eight graphical processor units by a factor of 94. For a reconstruction of the reflectivity with 64 layers of 10242 pixels we reduce the computing time from 33 hours to about 21 minutes. In a first clinical study and the images of two healthy probands the observed structures in breasts due to 3D USCT are comparable to images obtained with a clinical MRT.