: In this study a two-dimensional CFD code has been used to solve an unsteady flow problem in the free falling of cylindrical particles in the intermediate Reynolds Number ( 1 ? Re? 50) .shape of the particles that is used in the Initial value problem in a vertical channel for the free falling were circular, square and rectangular cylinders. Fluid flow is computed by the Navier-Stokes equations for moderate Reynolds numbers. The particles are moved at the effect of hydrodynamic forces, gravity and buoyancy forces. The governing equations for particle included second Newton law and torque have been exerted over particle. As the Reynolds Number increases a circular particle can be said to experience five different Irregular oscillation and periodic oscillation of the particle. The particle-fluid interaction is treated by Introducing a fully two dimensional Overset grid Scheme. Overset grid Scheme allows each component of a flow to be treated accurately and efficiently. In this method, fluid and particle have two independent grids (one Cartesian grid for fluid and other ones for particle (a Body fitted grid)). The governing flow equation (N.S) is solved in two grids then in the special points which are called “fringe points” and the fluid information is interpolated. There are a lot of methods for interpolating information between two grids such as: Bilinear, Bi cubic, triangular and etc. The flow over a fixed circular cylinder problem on Re=20 are available theoretically, numerically and experimentally. At the first, for validation CFD code, the flow over a fixed circular cylinder is solved and is compared. The results obtained were in good agreement to available previous data in the paper literature. Then it is solved the problem of free falling circular cylinder in Reynolds ( 0.5?Re 50) . The results compared with available ones ,were in good agreement to them. At the second part of this paper free falling square and rectangular cylinders is solved in channel and compared its results with curve fitting results Propacher et al. at the another part of this paper free falling of two rectangular and square cylinders simulations were also treated,. The flow in the several different channels is investigated. At the end, the solution of the heat transfer equation is developed in the CFD code. Key words: free falling, Overset grid, cylindrical particle, body fitted grid, interpolation.