Bluff bodies such as circular and square cylinders are the most important flow models in the aerodynamics, hydrodynamics and fluid mechanics due to their academic significance and engineering applications. The flow around cylinders has received a great deal of attention in many practical engineering applications such as flow around buildings, chimneys, marine structures, tall structures, suspended bridges, towers and pylons. In this research, large eddy simulations are performed to study fluid flow and heat transfer over a wall-mounted rectangular cylinder (three dimensional geometry) at a Reynolds number, Re = 12000. The cross-sectional aspect ratio is selected as b/a = 1-4, where a and b are the cylinder width and length, respectively. The height aspect ratio is h/a=7, (h/a, height to smaller cylinder side). The focus is given on the influence of b/a on the mean and instantaneous flow structures, strouhal number (St), and aerodynamic mean forces and their fluctuations. In addition, fluid flow and heat transfer over a two-dimensional rectangular cylinder (two dimensional geometry) with aspect ratio of b/a=1,2,3,4, (b/a, length to with of cylinder cross-section) were studied using K- -SST turbulence model at Re = 12000. All two and three-dimensional simulations were performed using ansys fluent. Grid size effect study in two and three dimensional simulations have been performed and suitable grids have been introduced. The results of this research show that aspect ratio of cylinder has an important role on the mean and instantaneous flow patterns and global parameters such as mean and RMS of lift and drag, strouhal and nusselt numbers. The results of two dimensional simulations have been compared and validated with other numerical and experimental researches that show good agreements in results of present work with reported ones. Furthermore, for three dimensional simulations with LES, the results of b/a=1 have been validated with available experimental and numerical results which show proper agreements. Results of this research showed that the global parameters and flow patterns for three dimensional geometry are totally different from those of two dimensional geometry due to effects of two ends of wall-mounted cylinder. In general, the results of infinite cylinder are not extendable for three dimensional cylinder although a few similarities are observed qualitatively in some cases. Keywords: Finite wall-mounted rectangular cylinder, Infinite rectangular cylinder, Two and three dimensional simulation, Aspect ratio, Turbulent flow hy;, Large eddy simulation (LES), Heat transfer, Vortex shedding