A theoretical study is presented on the response of a vertical array of hydrophones to shallow‐water signal and noise fields. A normal‐mode propagation model was used to provide the incident signal field. The field due to wind‐generated noise was obtained from a recently developed model based on wave theory. Two methods of combining hydrophone outputs are investigated: broadside beamforming and a mode‐matching approach. In the first case, limitations to signal gain are found due to the propagation properties of the shallow water environment. The highest gains are achieved with an array of length 15λ to 30λ. The second method involves applying amplitude and phase weightings in accordance with the shape of the largest signal mode. This enhances the signal gain for arrays longer than 8λ. The values of signal gain are primarily dependent on range and bottom type. The noise gain is found to be very dependent on sound speed profile; noise is rejected by a broadside array to a greater extent in summer conditions than in winter. Overall results for shallow‐water array gains show degradation from deep‐water gains of between 8 and 20 dB for a 20λ array for the cases studied.