The Lattice Boltzmann Method (LBM) is based on the kinetic theory of gases and is a powerful tool in computational fluid dynamics, which is beginning to gain widespread acceptance due to its simplicity and efficiency in modeling various physical processes. This paper discusses the application of LBM to numerically study the flow past cylindrical obstacles in a flat slot channel. Particular attention is paid to the influence of the cylinder position on the formation of the Karman street and the flow characteristics. The computational domain is a channel measuring 1000 by 100 cells, in which a cylindrical obstacle is placed. The center of the cylinder was successively installed in three positions: on the channel symmetry axis and with an upward offset. The simulation results showed that the displacement of the cylinder from the central axis of the channel significantly affects the vortex street parameters. When the cylinder was shifted, a change in the flow structure was observed. This is explained by the asymmetric distribution of the flow velocity around the cylinder when it is shifted toward the channel wall, which leads to a change in the vortex separation conditions. The obtained results demonstrate the influence of the obstacle position on the formation and evolution of vortices and confirm the efficiency of the LBM method for modeling such problems. The flow around the obstacle system is also presented. This study contributes to a deeper understanding of the mechanisms of the Karman vortex street formation and can be useful in the design of cooling grates and other engineering systems where it is necessary to take into account the interaction of the flow with heated structural element . Thus, the application of the lattice Boltzmann method in problems of modeling fluid flows taking into account complex geometric shapes and various boundary conditions demonstrates its high efficiency and potential for solving a wide range of engineering and scientific problems.