This research deals with the use of absorbing Markov chain which is one of means of processing the contingency cases in the determination and analysis of preparing the graduation of students. It also deals with the students who have been suspended. This process has been applied to the college of Science / University of Kirkuk. In particular the students in the of department of Mathematics and the students in the department of computing have been the focus of analysis. The purpose is baited up a concrete foundation for the future of the graduates of the college of Science. This is to get the maximum advantage of the outcomes of the college of Science order to meet the requirements of the society.The matrix designed for Mathematics shows that bribability any student to the second stage, then to third stage, finally to the fourth stage are given by 0.984, 0.982, and 0.988 respectively while the graduation has the probability of 0.990.With regard to the department of computing, the corresponding probability of passing to the second year, third year, and then graduation will have the probabilities 0.946, 0.988, 0.987 the 0.993. The reaming probabilities are allocated to the students who have been suspended.This procedure is regarded as one of the beast ways in analyzing the student mobility throughout his academic years of study in the college until he is graduated or he is suspended. Also estimate the time needed in each year and expect the number of students which ear be used on a key factor in order to get advantage of it by those who are the decision makers when setting the future development plan.