In this paper, a cubic objective programming problem (COPP)is defined, which is in the form of multiplying three linear functions. The simplex method is modified to solve a cubic objective programming problem. An algorithm for its solution is suggested. The algorithm of the usual simplex method is also reported. A vital application talks about how the developed algorithm can be utilized to unravel non-linear. The proposed technique can be illustrated with the constructed numerical examples and it showed steps by tables. The results of the study indicate that the new technique, modified simplex, gets the same result which is exactly similar to other methods such us (quadratic, linear simplex method).