This paper presents numerical results of the Gauss-Newton minimization algorithm application to inversion of an orientation of the metallic object with an oblong form. The Method of Auxiliary Sources (MAS) is used to obtain the synthetic data of the electromagnetic induction (EMI) in conducted numerical investigations. In the studies, presented here, it is assumed that electromagnetic and geometrical parameters of the object, such as conductivity, magnetic permeability, dimensions and the distance between the sensor and object's center are known. The approach is applied on inversion of object's orientation using noisy and noisy free synthetic data.