In this paper, a static-sample magnetometer is presented to measure the relative permeability of weakly magnetic materials. The method consists of scanning the magnetic field inside a dipole magnet by using an NMR teslameter to measure the perturbation of a test specimen on the externally applied field. Then, an inverse problem is used to compute the specimen's relative permeability. As a case study, the measurement of three different materials with different shapes and dimensions is carried out. The method was validated by measuring the same material by a vibrating sample magnetometry as proposed by the standard ASTM A342/A342M-14. The Monte Carlo evaluated expanded measurement uncertainty of the relative permeability is about 10 −4 for all the cases, with a level of confidence of 95 %. Index Terms-Magnetic measurements, inverse-problem approach, relative permeability, weak magnetic materials, NMR teslameter, stainless steel, vibrating sample magnetometer, tungsten I. INTRODUCTION I N alloys such as austenitic stainless steels, brass and bronze, weak traces of martensite are present [1]. Among pure metals, aluminium is the reference for these kinds of applications, though its mechanical properties are often inadequate for specific tasks or applications. Titanium is a valid alternative, but its high cost makes it only usable for specific applications (e.g., vacuum chambers). Finally, as an alternative to metals, ceramics have lower susceptibility, but they are often too brittle to be employed instead of metals. A good compromise among all these requirements is stainless steel. In particular, austenitic stainless steels are broadly used in harsh environments, such as nuclear reactors, naval vessels, and chemical plants, where the combination of good corrosion resistance with suitable mechanical properties is crucial.