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We consider a real massless scalar field inside a cavity with two movingmirrors in a two-dimensional spacetime, satisfying Dirichlet boundary conditionat the instantaneous position of the boundaries, for arbitrary and relativisticlaws of motion. Considering vacuum as the initial field state, we obtainformulas for the exact value of the energy density of the field and the quantumforce acting on the boundaries, which extend results found in previous papers.For the particular cases of a cavity with just one moving boundary,non-relativistic velocities, or in the limit of infinity length of the cavity(a single mirror), our results coincide with those found in the literature.

Quantum radiation reaction force on a one-dimensional cavity with two relativistic moving mirrors