This paper presents a new method for solving the inverse kinematics of robot manipulators symbolically using computer algebra. The kinematics equations, including the trigonometric functions of joint displacements, are expressed as multivariate polynomial equations by transforming these functions into variables. The multivariate polynomial equations can be solved by evaluating their reduced Grobner basis. The properties for efficient evaluation of the reduced Grobner basis and the inverse kinematics of a robot, whose last three joint axes intersect at a point, are shown. This procedure is implemented using Maple V and built into ROSAM (Robot Symbolic Analysis, by Maple) that is a robot analysis library made by our group. An analysis example of a structurechanged PUMA type robot is given.