This thesis presents a numerical study of laminar flow past a circular cylinder confined in the spanwise direction, motivated by applications in biomedical devices. The objective is to investigate the influence of vertical confinement on the transition to unsteady flow and determine the critical Reynolds number at which vortex shedding occurs. The study employs the Lattice Boltzmann Method (LBM) for fluid flow simulation, implemented using modern C++ parallel computing techniques to optimize performance on GPUs. A series of 2D and 3D simulations were conducted, systematically varying confinement levels to analyze their effect on flow behavior. The results demonstrate that increased confinement significantly impacts vortex shedding, delaying the onset of unsteadiness. Experimental validation confirms the accuracy of the numerical model, while performance analyses highlight the efficiency of GPU-based computation. The findings contribute to the optimization of microfluidic device designs, particularly in applications requiring controlled fluid mixing.