Several numerical computation algorithms exhibit dependences that lead to a wavefront of the computation. Depending on the data distribution chosen, pipelining communication and computation can be the only way to avoid a sequential execution of the parallel code. The computation grain has to be wisely chosen to obtain at the same time a maximum parallelism and a small communication overhead.On the other hand, when the size of data exceeds the memory capacity of the target platform, data have to be stored on disk. The concept of out-of-core computation aims at minimizing the impact of the I/O needed to compute on such data. It has been applied successfully on several linear algebra applications.In this paper we apply out-of-core techniques to wavefront algorithms. The originality of our approach is to overlap computation, communication, and I/O. An original strategy is proposed using several memory blocks accessed in a cyclic way. The resulting pipeline algorithm achieves a saturation of the disk resource which is the bottleneck in out-of-core algorithms.