The systems of difference equations describing two possible current configurations of linear vortex in the 3D ordered Josephson medium based on the conditions of fluxoid quantization in the cells are obtained. The theoretical investigation was realized on the assumption that magnetic field in a cell is not homogeneous.

A method of exact solutions of the systems in case of both configurations of linear vortex for all values of parameters is proposed. The current configurations for linear vortex as well as the values of full energies of both configurations are calculated.