© Springer International Publishing Switzerland 2015. We propose two randomized tensor algorithms for reducing multilinear tensor rank. The basis of these randomized algorithms is from the work of Halko et al. (SIAM Rev 53(2):217–288, 2011). Here we provide some random versions of the higher order SVD and the higher order orthogonal iteration. Moreover, we provide a sharp probabilistic error bound for the matrix low rank approximation. In consequence, we provide an error bound for the tensor case. Moreover, we give several numerical examples which includes an implementation on a MRI dataset to test the efficacy of these randomized algorithms.