Aims.We study fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma slabs in a uniform magnetic field. This allows us to analyse in a simple configuration the collective behaviour of the structure due to the interaction between the slabs. Methods: .We first calculate the normal modes of the system and find analytical expressions for the dispersion relation of the two-slab configuration. Next, we study the time-dependent problem of the excitation of slab oscillations by numerically solving the initial value problem. We investigate the behaviour of the system for several shapes of the initial disturbances. Results: .The symmetric mode respect to the centre of the structure is the only trapped mode for all distances between the slabs while the antisymmetric mode is leaky for small slab separations. Nevertheless, there is a wide range of slab separations for which the fundamental symmetric and antisymmetric trapped modes are allowed and have very close frequencies. These modes are excited according to the parity of the initial perturbation. Conclusions: .We find that for any initial disturbance the slabs oscillate with the normal modes of the coupled slab system, which are different from the modes of the individual slabs. We show that it is possible to excite the symmetric and antisymmetric trapped modes at the same time. This kind of excitation can produce the beating phenomenon, characterised by a continuous exchange of energy between the individual slabs.