  We studied the two-qubit quantum Rabi model and found its dark state
solutions with at most N photons. One peculiar case presents when $N=3$, which
has constant eigenenergy in the whole coupling regime and leads to level
crossings within the same parity subspace. We also discovered asymptotic
solutions with at most $N=2i+3$ $(i=1,2,3,\dots)$ photons, and constant
eigenenergy $N\hbar \omega$ when coupling $g$ becomes much larger than photon
frequency $\omega$. Although generally all photon number states are involved in
the two-qubit quantum Rabi model, such $N$-photon solutions exist and may have
applications in quantum information processing with ultrastrong couplings.
