This paper presents a new technique to analyze dynamic behaviour of a sticker rod string used in the oil well industry. The main concept of the proposed approach is to replace the actual complicated system by a simpler one. This needs the output or one-time accurate Solutions of the actual system. This problem is solved using D'Alembert's solution of systems equation and the adaptive filter matrix method developed by the authors. The developed Computer program performs the Calculations in very short real time with reasonable accuracy, and without extensive hardware and software requirements. It has been proven that it is possible to use the transfer matrix to calculate load-displacement relations a hundred or more times in one stroke. This could be very advantageous in building new well-head controllers and other tools to control the oil wells.