pyDNTNK is a software package for applying non-negative Hierarchical Tensor decompositions such as Tensor train and Hierarchical Tucker decompositons in a distributed fashion to large datasets. It is built on top of pyDNMFk. Tensor train (TT) and Hierarchical Tucker(HT) are state-of-the-art tensor network introduced for factorization of high-dimensional tensors. These methods transform the initial high-dimensional tensor in a network of low dimensional tensors that requires only a linear storage. Many real-world data,such as, density, temperature, population, probability, etc., are non-negative and for an easy interpretation, the algorithms preserving non-negativity are preferred. Here, we introduce the distributed non-negative Hierarchical tensor decomposition tools and demonstrate their scalability and the compression on synthetic and real world big datasets. Features: Utilization of MPI4py for distributed operation. Distributed Reshaping and Unfolding operations with Zarr and Dask. Distributed Hierarchical Tensor decompositions such as Tensor train and Hierarchical Tucker. Ability to perform both standard SVD based and NMF based decompositions. Scalability to Tensors of very high dimensions. Automated rank estimation with SVD for each stage of tensor decomposition. Distributed Pruning of zero row and zero columns of the data.