The multidimensional analysis based on data cube has been growing interest. However existing data cube model usually does not have the semantics of attributes and hence the analysis usually provides results with raw numbers and ignores the real meanings of these numbers. An example result is that the total sales of PC in this year are above 2000. The semantics of sale performance, high or low, is not clear and that is not easy to be understood for decision makers. The semantic data cube model with linguistic semantics is presented in this paper. The semantic data cube uses fuzzy set to represent the linguistic semantics of the dimensions and measures of data cube. The computation of semantic data cube is studied and the serial and parallel computation algorithms are presented. The experiments on the synthetic datasets show that the algorithms are scalable and efficient.