The majority of the failures of shell and tube heat exchanger tubes are reported due to the flow-induced vibration caused by shell side cross flow. Fluid elastic instability, vortex shedding, and turbulent buffeting are the excitation mechanisms responsible for the failure of the tubes. The failure occurs due to tube-to-tube impacts leading to impaction marks on the tube surface and, subsequently, leading to the failure due to fretting wear and fatigue. The present research work deals with the determination of critical velocity at instability for rotated square finned tube arrays subjected to water cross flow. In all, total six tube arrays are tested with two different pitch ratios, each with a plain tube array, a coarse finned tube array, and a fine finned tube array. Pitch ratios considered in the study are 2.1 and 2.6, while fin densities considered are coarse (4 fpi = 6.35 mm) and fine (10 fpi = 2.54 mm). The effect of array pattern, pitch ratio, and fin density on the onset of instability is studied by conducting experiments in the water cross flow. The effect of tube array pattern is studied by comparing the results of the present study with authors' published results for parallel triangular finned tube arrays in the water cross flow. The study led to the conclusion that the instability threshold is delayed for rotated square tube arrays compared to parallel triangular tube arrays. It is also observed that instability thresholds for coarse and fine finned tubes are delayed compared to plain tubes and is found to be more for finned tubes with higher fin densities.