The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. However, the K shortest hyperpaths problem has not yet been investigated.In this paper we present procedures for finding the K shortest hyperpaths in a directed hypergraph. This is done by extending existing algorithms for K shortest loopless paths. Computational experiments on the proposed procedures are performed, and applications in transportation, planning and combinatorial optimization are discussed.