The study aims at showing the impact of the flexible organizational structure on the knowledge lift in the academic leadership in a selected sample of the Iraqi universities that represent the top of the educational pyramid from the administrative and scientific point of view. The study problem is focused on obtaining an appropriate organizational structure that helps to increase knowledge raising, the researcher considered the formulation of the problem with a series of questions:1. Do academic leaders have an idea of the importance of flexible organizational structure in educational organizations?2. Is there a relationship between the dimensions of the flexible structure and the distance of the knowledge lift? The following hypotheses were selected based on the findings of the study1. The existence of a significant correlation between the flexible organizational structure and the cognitive lift according to the value of the correlation coefficient. The correlation ratio at the level of each university according to the correlation coefficient value was the university book college in the first place, the pen college university in second place, Ranked third.2. The existence of a relationship of significant significance for the dimensions of the flexible organizational structure in the dimensions of the knowledge lift according to the regression coefficient and the T (F) and the (F) The University ranked second, followed by the University of Kirkuk ranked third. Based on the hypotheses of the study, objectives, importance and implications of the study and the purpose of relationships and impact between the variables and the validity of the hypotheses was used a number of statistical tools and based on the statistical program Spss Version 19) to conduct the analysis and the analytical statistical tools are as follows: Test (F), (T) Simple linear regression, simple correlation, and descriptive statistical instruments are as follows: arithmetic mean, percentages, standard deviation, variance and response rate. The selection of the field side was based on the selection of three universities (University of Kirkuk, Faculty of Pencil, University College of Writers), a field of study and testing of hypotheses, and distributed (112) questionnaire question naira on a sample of academic leaders and analyzed, the study reached a number of conclusions and recommendations, The mutual influence between the flexible organizational structure and the cognitive leveraging helps to absorb the future regulatory changes that are continuous according to the internal and external variables required by the effective organizational structure. The most important recommendations are the adoption of flexible organizational structures that allow for increased knowledge Matt researched.