With the rapid improvement of computer technology, Visual-based sensors have gained an intense popularity and consequently have begun to be utilized extensively in robotic research. Among the various applications in robotics, one of the most popular concepts is gathering information from the navigation environments for mobile robots by working on optical flow of vision which is derived from a stereo camera located on the robots. We can determine from the optical flow the movement of the objects within the area of robotic vision. If a relative motion in the environment, whether from objects or the mobile robot, is present, then the information that can be gathered from this environment is enough for the mobile robot to execute its obstacle detection and avoidance behaviors. Optical Flow is a concept which has been worked on for quite a long time. But due to problems which prevail on all visual based applications, such as computing difficulties and slow rate of getting results, researchers have come across with so many difficulties that deter them from use in real time applications, especially in robotics. But as the latest research and techniques have come to view, new practical methods were put forward. In this study, by making use of optical flow calculation and multi layer perceptron Artificial Neural Network, a methodology has been tried to be put forward for mobile robot obstacle detection and avoidance behavior. The study of methodology has been supported by experimental results that were obtained from Matlab simulation environments. The images of the views were taken from the real navigation environment and then optical flow calculations for all images were obtained via matlab simulink blocks that were created in advance, as an algorithm which can calculate optical flows from stereo visions. As optical flows of each pair of stereo views were derived, a data base was constituted in order to train the multi layer perceptron. By the help of the data set and the Levenberg- Marquardt learning algorithm, a neural network which was well trained in Matlab environment in order to detect the presence of obstacles was created. Experimental results, obtained during the study have strengthened the ideas which have supported the usage of the Optical Flow via Artificial Neural Network in mobile robotics for obstacle detection and avoidance behaviors.