The study of sectional curvature is considered an important study as it is used in many sciences such as engineering, physics and mathematics. Sectional curvature has several types, including positive, non-positive (negative) and non-negative sectional curvature. This study deals with non-positive sectional curvature and is considered an addition to what was presented in this field .The aims of this paper is to calculate the non-positive sectional curvature by using Matlab. It also aims to find some applications of non-positive sectional curvature .We followed the applied mathematical method using Matlab. Also we showed the calculation of Non –Positive Sectional Curvature using Matlab and their some applications by following descriptive approach in order to achieve the stated objectives of the paper, and we found the following some results: Matlab gives precise results of high speed compared with that of Manual, Also stated the ability and capability of Graphs or Diagram drawing to any curvature via Matlab. Explained the possibility of the calculation of Non –Positive Sectional Curvature by Matlab with a very high rate and accuracy also shed lights on as Cartan –Hadamard theory which is considered one of the most important applications regarding Non –Positive sectional curvature.