In this paper, a solution is given to the problem of dead-beat ripple-free tracking for a multivariable multirate sampled-data system. The solution of such a problem is reduced to the solution of a dead-beat tracking problem for the corresponding discrete-time periodic system by introducing an additional requirement of dead-beat control for the control input of the multirate sampled-data system. The conditions for the problem solvability include the existence of a continuous-time internal model of all reference signals in the continuous-time plant. The design procedure of the periodic discrete-time compensator reduces to the design of a dead-beat periodic controller.