In this work, an application of the algebraic reconstruction technique to a borehole reconstruction problem is considered. The formulation of the borehole problem gives the attendant electromagnetic wave equations in matrix form. The algebraic reconstruction technique is used to reconstruct a solution. Three sources of errors are identified in the reconstruction process. Suggestions are made which will help minimize or predict the effects of these errors. General limitations of the algebraic reconstruction technique are discussed. The limitations in terms of the borehole problem are explained. Practical limitations for the borehole problem are thus obtained and quantified mathematically. It is found that even in some practical situations, the borehole reconstruction process is impossible.