The aim of this paper is to determine the stress levels at the end of a long slender shaft such as a drilling assembly used in the oil or gas industry using a mathematical model in real-time. The torsional deflection experienced by this type of drilling shaft (about 4 KM length and 20 cm diameter hollow shaft with a thickness of 1 cm) can only be determined using a distributed modeling technique. The main objective of this project is to calculate angular velocity and torque at the end of the shaft by TLM method and also analyzing of the behavior of the system by transient response. The obtained result is compared with lumped modeling technique the importance of these results will be evident only after the mentioned comparison. Two systems have different transient responses and in this project because of the length of the shaft transient response is very important. Keywords—Distributed Lumped modeling, Lumped modeling, Drill string, Angular Velocity, Torque. I. INTRODUCTION RILLS used in oil/gas industry are good examples of long slender shafts where the ratio of shaft's length to its diameter is very large. In Oil/gas well drilling the drill strings transmits torque to the drill bit for cutting the wells. Drill shaft failure (due to torsional stress), friction, vibration and risk of the operation are increased as the drill string length increases. Stress level monitoring during drilling operations increases the efficiency of the drilling and it is the most effective methods to prevent threat of the drill failure (8). Most of the existing stress / torque monitoring system use sensors to provide information from down hole during drilling. This information is transferred to the surface and after being analysed and processed it enables engineers to control system. The use of sensors is very costly and existing modelling tools such as finite element technique are computationally very slow for real-time prediction. On the other hand the lumped modelling techniques are too simplistic to give an accurate prediction of the load torque at the other end of the shaft. Using mathematical modelling technique a virtual sensor can be developed. Distributed lumped modelling technique can be employed to predict the stress level at the load end of the shaft accurately.In this paper, the distributed lumped modelling technique which has been extended to mechanical systems modelling is adapted to the drill string modelling by measuring angular velocity and torque at end of the drill string. And also a comparison of the simulation of the distributed lumped modelling and lumped modelling are presented.