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A multinorm one torus associated to a commutative \'etale algebra $L$ over aglobal field $k$ is of Kummer type if each factor of $L$ is a cyclic Kummerextension. In this paper we compute the Tate-Shafarevich group of such toribased on recent works of Bayer-Fluckiger, T.-Y. Lee and Parimala, and ofT.-Y.~Lee. We also implement an effective algorithm using SAGE which computesthe Tate-Shafarevich groups when each factor of $L$ is contained in a fixedconcrete bicyclic extension of $k$.

Computing Tate-Shafarevich groups of multinorm one tori of Kummer type