  We compute the partition function for 6d $\mathcal{N}=1$ $SO(2N)$ gauge
theories compactified on a circle with $\mathbb{Z}_2$ outer automorphism twist.
We perform the computation based on 5-brane webs with two O5-planes using
topological vertex with two O5-planes. As representative examples, we consider
6d $SO(8)$ and $SU(3)$ gauge theories with $\mathbb{Z}_2$ twist. We confirm
that these partition functions obtained from the topological vertex with
O5-planes indeed agree with the elliptic genus computations.
