Analytic 6-SPS parallel (Stewart platform) robots are 6-SPS parallel robots with characteristic polynomial of fourth degree or lower. In this paper, a method for generation of analytic 6-SPS parallel robots is put forward and two new classes of analytic 6-SPS parallel robots in addition to the analytic 6-SPS parallel robots already known are generated using the proposed method. The approach is based on that the forward displacement analysis of a 6-SPS parallel robot is equivalent to the configuration analysis of its corresponding 6-SS structure obtained by locking all the actuated joints of the robot and that the configuration analysis of a decomposable 6-SS structure can be reduced to those of its sub-structures which are always easier to deal with. Forward displacement analyses of the two new classes of analytic 6-SPS parallel robots are performed. It is shown that the characteristic polynomials are of second and fourth degree respectively and the maximum numbers of possible configurations are all equal to 8 for the two new classes of analytic 6-SPS parallel robots. All the solutions obtained from the forward displacement analyses are verified using a reverse displacement analysis.