A stable method for the determination of the nematic liquid crystal material parameters, such as the splay and bend elastic constants, the anisotropy of diamagnetic susceptibility, the electric permittivities and either the coupling between the nematic molecules and the substrate at the planar liquid crystal cell boundary (i.e. the director field boundary value), is presented in the work. The method consists of two stages: firstly the effective electric permittivity of planar nematics cell is measured as a function of external electric and magnetic fields, secondly the coefficient inverse problem is solved numerically using the experimental data to determine the values of material parameters. The coefficient inverse problem is posed in a variational way as a problem of nonlinear mean-square fit of the calculated nematics layer characteristics to the measured ones. The description of phenomena is based on Ericksen's - Leslie's theory. The unknown material parameters serve in this approach as the fit parameters, the best values of which corresponding to the best possible approximation of the experimental data by the refined mathematical model are to be found. The method was successfully used for the determination of the material parameters of PCB and can be applied to every nematics.