Control strategy based on generalized predictive controller (GPC) is proposed for control of electrical drives with transmission elasticity and backlash. Takagi-Sugeno fuzzy model is used for identification of the two-mass mechanical system with elastic transmission and backlash with negligible friction. It is assumed that only measurement at the load side is available. Since GPC controller requires linear process model, Takagi-Sugeno fuzzy model is linearized by means of instantaneous linearization in each sample instant. This control strategy is then compared to the classical GPC based on linear ARX model by computer simulations and experimentally on a laboratory model of the electrical drive with transmission elasticity and backlash.