Metal binder jetting (MBJ) is an additive manufacturing (AM) technology split into two process steps: printing and sintering. Firstly, product is built up layer-by-layer by the selective deposition of a binder agent on a powder bed. Secondly, a thermal treatment (sintering) consolidates the metal structure. MBJ is currently becoming more and more attractive on the reason of high potential scalability, cost-effective production and wide range of available material feedstocks. However, the transition towards industrial scale production is restrained by the critical control of dimensional and geometrical precision of parts after sintering operation. In fact, product geometry is affected by anisotropic dimensional change or even shape distortion. This study aims at investigating the dimensional and geometrical precision of through holes. Three sample geometries were designed, having a through hole with axis perpendicular to the building direction and located at different levels along sample height. Samples were measured by a coordinate measuring machine before and after sintering, in order to assess the shrinkage and any shape change. Results highlight the inhomogeneous volumetric and linear shrinkage of the three geometries, which is influenced by the printing position in the building plane. A macroscopic deformation of parallelepiped geometry was also evidenced, caused by the superposition of layer shifting originated on printing, and by the frictional forces between sample surface and alumina support during sintering. Such distortion significantly affects the shrinkage and form error of holes.