This paper investigates the neural network approach to solve the inverse kinematics problem of redundant robot manipulators in an environment with obstacles. The solution technique proposed requires only the knowledge of the robot forward kinematics functions and the neural network is trained in the inverse modeling manner. Training algorithms for both the obstacle free case and the obstacle avoidance case are developed. For the obstacle free case, sample points can be selected in the work space as training patterns for the neural network. For the obstacle avoidance case, the training algorithm is augmented with a distance penalty function. A ball-covering object modeling technique is employed to calculate the distances between the robot links and the objects in the work space. It is shown that this technique is very computationally efficient. Extensive simulation results are presented to illustrate the success of the proposed solution schemes. Experimental results performed on a PUMA 560 robot manipulator is also presented.