Abstract : Our research work aims at developing ultrasound tomography applied to breast imaging. Near-field tomographic solutions are introduced to solve the imaging problem of soft tissues assumed to be weakly heterogeneous _Born approximation_ and excited by spherical waves. The solution to the forward problem is based on the Huygens-Fresnel principle which describes the scattered field as the result of the interference scheme of all the secondary spherical waves. From the derivation of the scattered field, a new Fourier transform that has been called the elliptical Fourier transform is defined: It differs from the standard Fourier transform in that instead of a plane wave decomposition, a harmonic ellipsoidal wave decomposition is obtained. Based on this spectral analysis, a near-field radon transform is designed that complements the “far-field tools” published in diffraction tomography literature. Then, assuming that the measuring distance is greater than one wavelength, the feasibility of reconstructing either the impedance or the velocity maps of an acoustical _perfect fluid_ model is demonstrated. Healthy and pathological breast phantoms are designed and numerical simulations were performed which confirmed the advantages of the tomographic approach as compared to conventional ultrasounds.