  A simplicial complex $\Delta$ is a virtually Cohen-Macaulay simplicial
complex if its associated Stanley-Reisner ring $S$ has a virtual resolution, as
defined by Berkesch, Erman, and Smith, of length ${\rm codim}(S)$. We provide a
sufficient condition on $\Delta$ to be a virtually Cohen-Macaulay simplicial
complex. We also introduce virtually shellable simplicial complexes, a
generalization of shellable simplicial complexes. Virtually shellable complexes
have the property that they are virtually Cohen-Macaulay, generalizing the
well-known fact that shellable simplicial complexes are Cohen-Macaulay.
