This paper presents the implementation of a new method for lossless compression of hyperspectral images for novel parallel environments. The method in question is an interband version of the linear prediction approach for hyperspectral images. The interband linear prediction method consists of two stages: predictive decorrelation that produces residuals and the entropy coding of the residuals. The results and comparisons with other methods are discussed. The speedup of the thread version is almost linear with respect to the number of processors.