In radiology practices, the ultrasound-guided breast biopsy is among the most commonly performed minimally invasive procedures. However, many radiology residents in their graduate residencies are found with little or no hands-on experience with ultrasound-guided breast procedures. To enhance safety, the problem can be solved by the use of anthropomorphic training phantoms which can provide the resident with realistic ultrasound imaging and needle insertion haptic feedback. Stiffness and acoustic properties of breast tissues vary between different people. The training breast phantom should be able to possess different acoustic and mechanical properties which conform the inconsistencies found in real tissues among people. Therefore, this paper investigates the tunability of acoustic and mechanical behaviors in breast tissue mimicking materials (TMMs). Experiments of central composite design (CCD) with a center point, four corner points, and an additional four axis points were used to fit the non-linear regression model of the speed of sound. The same design of experiment approach was then used to fit the second-order response surface of the attenuation coefficient. Suitable series of tissue mimicking materials for the glandular tissue and malignant lesion were suggested. Latin hypercube design method was conducted to evaluate the main factors that affected the mechanical property (Young's modulus) of tissue mimicking materials. The results showed that the recipe of tissue mimicking materials could be customized to possess different acoustic and mechanical properties which conform the inconsistencies found in real breast tissues.