Large eddy simulations (LES) are performed at low Reynolds number (2000–6000) to investigate the dynamic fluid-elastic instability in square normal cylinder array for a single-phase fluid cross flow. The fluid-elastic instability is dominant in the flow normal direction, at least for all water-flow experiments (Price, S., and Paidoussis, M., 1989, “The Flow-Induced Response of a Single Flexible Cylinder in an in-Line Array of Rigid Cylinders,” J. Fluids Struct., **3**(1), pp. 61–82). The instability appears even in the case of single moving cylinder in an otherwise fixed-cylinder arrangement resulting in the same critical velocity (Khalifa, A., Weaver, D., and Ziada, S., 2012, “A Single Flexible Tube in a Rigid Array as a Model for Fluidelastic Instability in Tube Bundles,” J. Fluids Struct., **34**, pp. 14–32); Khalifa et al. (2013, “Modeling of the Phase Lag Causing Fluidelastic Instability in a Parallel Triangular Tube Array,” J. Fluids Struct., **43**, pp. 371–384). Therefore, in the present work, only a central cylinder out of 20 cylinders is allowed to vibrate in the flow normal direction. The square normal (90 deg) array has 5 rows and 3 columns of cylinders with 2 additional side columns of half wall-mounted cylinders. The numerical configuration is a replica of an experimental setup except for the length of cylinders, which is of 4 diameters in numerical setup against about 8 diameters in the experiment facility. The single-phase fluid is water. The standard Smagorinsky turbulence model is used for the subgrid scale eddy viscosity modeling. The numerical results are analyzed and compared to the experimental results for a range of flow velocities in the vicinity of the instability. Moreover, instantaneous pressure and fluid-force profiles on the cylinder surface are extracted from the LES calculations in order to better understand the dynamic fluid-elastic instability.