A study of the local interstellar medium (LISM) using a robust inversion method, similar to current tomography techniques, is applied to compiled data on neutral interstellar absorbers and Hipparcos parallaxes. We present here the 3-D distribution of two neutral species, NaI and HI. Our analysis enables us to obtain a reliable 3-D density distribution of the IS matter in the solar neighbourhood, providing a new basis for the discussion of origin, present state and evolution of the LISM. We show that neutral IS matter is distributed in compact clouds or in cloud complexes with cavities between them. It is now easy to distinguish the so-called Local Bubble and the Loop I cavities and also two tunnels linking the Local Bubble to the outer regions of the galaxy, away from the galactic plane. Better accuracy is achieved for NaI, as to a larger number of lines-of-sight and target stars than are available for HI. A rather detailed NaI 3-D density distribution is obtained with a 40 pc smoothing length. The extended high-density regions in the NaI and HI maps are correlated which is not the case for the diffuse regions. The density ratio rho_HI /rho_NaI is lower or equal to 9.1.10⁸ +/- 3.10⁸ for extended high density clouds. Using observations from the ESA Hipparcos space astrometry mission.