The 12UPS parallel mechanism with fully redundant actuation was constructed on the basis of the Stewart platform and the analysis of linear correlation of constraint screws of active inputs in redundant actuation parallel mechanism. By comparing the differences of electric drive and hydraulic drive, the electrohydraulic drive mode was determinded to be used suitably. The influence coefficient method was applied to establish the dynamic models of the mechanism. In order to distinguish electric cylinder and hydraulic cylinder in processing, zero internal forces were considered as constraint conditions when optimizing the driving forces. The KuhnTucker theorem was applied to study the driving forces optimization procedure of mechanism, withing the minizied quadratic sum of driving forces and the minizied quadratic sum of the driving power respectively. The numerical example shows that the optimization method using minimizing the quadratic sum of drive powers is the best under the condition of zero internal forces. This optimization method can not only fully exert the merits of electric and hydraulic drive but also avoid its disadvantages, so it is applicable to the parallel mechanism with electrohydraulic drive and fully redundant actuation.