The k-ary n-cube is one of the most attractive interconnection networks for parallel and distributed computing systems. In this paper, we investigate hamiltonian cycle and path embeddings in k-ary n-cubes Q(n)(k) based on structure faults, which means each faulty element is isomorphic to any connected subgraph of a connected graph. Let H be a connected graph with HI {K1, K1,1, K1,2, K1,3}. We show that for two arbitrary distinct healthy nodes of a faulty Q(n)(k), there exists a fault-free hamiltonian path connecting these two nodes if the number of faulty element is at most a certain number and each faulty element is isomorphic to a connected subgraph of H. We also show that there exists a fault- free hamiltonian cycle if the number of faulty element is at most a certain number and each faulty element is isomorphic to a connected subgraph of H. These results mean that the k-ary n-cube Qnk can tolerate up to 4(n - 2) faulty nodes such that Q(n)(k) - V(F) is still hamiltonian and hamiltonian-connected, where F denotes the faulty set of Q(n)(k).