Breast physical phantoms are a basic tool for the assessment and verification of performance standards in daily clinical practice of x-ray breast imaging modalities. They are also invaluable in testing and evaluation of new x-ray breast modalities to be potentially established, e.g. breast computed tomography, dual-energy breast CT and phase-contrast mammography and tomography. Nowadays, there is a lack or there are only a limited number of breast physical phantoms available for this purpose. The aim of this study is to explore a range of 3D printing materials such as resins, PLA, ABS, Nylon etc, to determine their attenuation and refractive properties, and to finally compare them to the properties of the breast tissues: adipose, glandular and skin. To achieve this goal, step-wedge phantoms were computationally modeled and then manufactured using stereolithographic and fused-deposition modeling technologies. X-ray images of the phantoms were acquired, using monochromatic beam at ID17, ESRF, Grenoble for three energies-30 keV, 45 keV and 60 keV. Experimental data were further processed to obtain the linear attenuation coefficients of these materials. Comparison with theoretical data for the linear attenuation coefficients and the refractive indexes for breast tissues was performed. From the studied materials, most of the resins, Nylon, Hybrid, PET-G show absorption properties close to the glandular tissue, while ABS shows absorption characteristics close to these of the adipose tissue. For phase-contrast imaging, it turns out that the ABS combined with resin-based materials to represent the adipose and glandular tissues, respectively may be a good combination for manufacturing of a phantom suitable for these studies. These results can be used for the design and the construction of a new physical anthropomorphic phantom of the breast with improved anatomical and radiological characteristics dedicated for advanced mammography imaging techniques implemented at higher photon energies.