This paper addresses the kinematic modelling, solutions and trajectory planning of a tele-laparoscopic manipulator. This type of manipulator can be used in remote positioning of laparoscopic tools through tele-operating system. Specifically the paper models kinematics of a typical manipulating system which can be used in such tele-surgery. Inverse kinematics solutions are also obtained for two kinematically constraint motions which are part of a typical trajectory of the laparoscopic tools. These are fixed axis rotation of the tool and its
straight line motion. Simulation results are presented to demonstrate the validity of such models and solutions.