The BSCCO type intrinsic Josephson junction has been modeled as a stack of inductively coupled long Josephson junctions, which were described by a system of coupled sine-Gordon equations. In a system of 10 long Josephson junctions coupled to a linear cavity, we numerically investigate how the cavity perturbs fluxon motion in the junctions. Fluxons in neighboring junctions are repulsive leading to anti-phase motion. The cavity provides a force which perturbs this anti-phase motion, and may even force the fluxons to build a square lattice, i.e. to perform in-phase motion. For different values of the inductive coupling strength, we investigate the cavity current, fluxon phase difference, and current–voltage characteristic. The stack-cavity system with in-phase fluxon motion may be utilized as a THz oscillator.