A method is presented to analyse wave interactions with an array of simplified wave energy devices. The problem is formulated in terms of a group of heaving vertical circular cylinders floating in the ocean, whose motion is damped by their power take-off mechanisms. Under the assumptions of linear wave theory, an exact analytical solution is derived in order to compute wave and body motion amplitudes. From these, the hydrodynamic heave exciting force, the added mass and damping coefficients, and the power extracted by each element of the array are calculated and presented as functions of incident wave number. The numerical implementation proved particularly efficient and the results compare very well with other theoretical and experimental work.