In this paper the solution algorithm of the inverse kinematics problem for IRB-1400 robots is presented. This algorithm may be a basic component of future computational intelligence for theses robots. The problem of computing the joint variables corresponding to a specified location of the end-effector is called the inverse kinematics problem. This algorithm may be used with the current computer control algorithms for these robots. It would allow controlling these robots through the use of the vision system, which specifies the required location of the end-effector. This required location makes it possible for the end-effector to approach an manipulation object (observed by the vision system) and pick it up. These robots are equipped with several manipulator which has 6 links connected by the revolute joints. First the location of the end-effector in relation to the base of the manipulator is described. Next the analytical formulas for joint variables (dependent on these location) are derived. These formulas have take into account the multiple solutions for the singular configurations of this manipulator.