  We propose a scheme to entangle multiple material qubits through interaction
with single photons via non-exciting processes associated with strongly
coupling systems. The basic idea is based on the material state dependent
reflection and transmission for the input photons. Thus, the material qubits in
several systems can be entangled when one photon interacts with each system in
cascade and the photon paths are mixed by the photon detection. The character
of non-exciting of the material qubits does not change the state of material
qubit and thus ensures the possibility of purifying entangled states by using
more photons under realistic imperfect parameters. It also guarantees directly
scaling up the scheme to entangle more qubits. Detailed analysis of fidelity
and success probability of the scheme in the frame of an optical
Fabry-P\'{e}rot (FP) cavity based strongly coupling system is presented. It is
shown that a two-qubit entangled state with fidelity above 0.99 is promised
with only two photons by using currently feasible experimental parameters. Our
scheme can also be directly implemented on other strongly coupled system.
