Excessive exposure to radiation increases the risk of cancer. We present the concept and design of a new imaging paradigm, X-ray induced acoustic computed tomography (XACT). Applying this innovative technology to breast imaging, one single X-ray exposure can generate a 3D acoustic image, which dramatically reduces the radiation dose to patients when compared to beast CT. A theoretical model is developed to analyze the sensitivity of XACT. A noise equivalent pressure model is used for calculating the minimal radiation dose in XACT imaging. Furthermore, K-Wave simulation is employed to study the acoustic wave propagation in breast tissue. Theoretical analysis shows that the X-ray induced acoustic signal has a 100% relative sensitivity to the X-ray absorption (given that the percentage change in the X-ray absorption coefficient yields the same percentage change in the acoustic signal amplitude), but not to X-ray scattering. The final detection sensitivity is primarily limited by the thermal noise. The radiation dose can be reduced by a factor of 100 compared with the newly FDA approved breast CT. Reconstruction result shows that breast calcification with diameter of 80 μm can be observed in XACT image by using ultrasound transducers with 5.5 MHz center frequency. Therefore, with the proposed innovative technology, one can potentially reduce radiation dose to patient in breast imaging as compared with current x-ray modalities.