The memory usage of sparse direct solvers can be the bottleneck to solve large-scale problems. This paper describes a first implementation of an out-of-core extension to a parallel multifrontal solver (MUMPS). We show that larger problems can be solved on limited-memory machines with reasonable performance, and we illustrate the behaviour of our parallel out-of-core factorization. Then we use simulations to discuss how our algorithms can be modified to solve much larger problems.