This paper describes a theoretical analysis of the ocean wave energy absorption by a periodic linear array of oscillating water columns (OWCs) of arbitrary planform. The analysis is based on classical linear water wave theory and uses the expressions for the wave field resulting from time-harmonic pressure distributions on the free surface. The water depth is assumed finite and constant. The cases of oblique and normal incidence are analysed. A linear power take-off mechanism is assumed, but a complex characteristic constant (allowing for phase control) and air compressibility are considered. Special analytical expressions are derived for OWCs of rectangular and circular planforms. Numerical results for circular chambers show that the hydrodynamic interaction can substantially change the maximum energy absorption, depending on array and chamber geometry and on angle of incidence.