This paper aims to apply adaptive filtering algorithms in sensor array processing for underwater surveillance and detection systems with linear arrays. Adaptive filters are iterative in nature and continuously update the filter taps to minimize the error signal based upon certain criterion. Adaptive filters are used in beamforming to place the main beam in the direction of desired signal and place nulls in the direction of unwanted signals. Adaptive filters are also used in spectral analysis of acoustic signals for background noise cancellation. This paper evaluates the performance of three adaptive filtering algorithms with respect to sensor array design parameters i.e. number of sensors, sensor spacing, number of incident signals and their angular separation. The three adaptive filtering algorithms namely least mean square (LMS), normalized LMS (NLMS), and sample matrix inversion (SMI) have been compared in the context of linear array beamforming. The paper provides detailed discussions on the simulation results of these adaptive algorithms in terms of convergence speed, beamwidth, null depths and maximum side lobe levels. In addition the paper illustrates a practical example of applying adaptive filters in underwater sensor array processing systems for detection of target’s acoustic signatures.