The investigation of wakes of bluff bodies in a channel is still relevant despite the large number of works devoted on it, in both experimental and numerical studies. This attractiveness is mainly due to its related applications and practical interest in varied engineering fields. The understanding of dynamic flow behavior and the topology of the instability structures occurring in the wake is essential in order to optimize the obstacle shape according to the desired objectives. A confined laminar flow around a square and a circle, placed in a channel is numerically investigated in this work using Lattice Boltzmann method. The study is then extended to 3D computations with horizontal cylinder within a square then a circular cross-section mounted inside a rectangular duct. The Reynolds number (Re), based on the maximum velocity and the cross-section height varies between 50 and 120 and the blockage ratio is r=1/3. This geometry is representative of a passive method to enhance mixing in the laminar channel flow. LBM was built up on the D2Q9 and D3Q19 model for respectively 2D and 3D computations. The single relaxation time approach called the lattice-BGK method was adopted. The topology of the vortex-shedding phenomena and wake behavior according the Reynolds numbers, for both geometries of the obstacle are focused. The effect of wall confinement on the flow transition to the vortex shedding regime is discussed. Velocity profiles and integral parameters such as recirculation length and Strouhal number were investigated. The numerical results are supported by literatures works results for the same configuration showing the performance of LBM as numerical tools simulation for such kind of flows.