The lattice Boltzmann equation (LBE) is an alternative kinetic method capable of solving hydrodynamics for various systems. Major advantages of this method are due to the fact that the solution for the particle distribution functions is explicit, easy to implement, and natural to parallelize. Such characteristics make this method a suitable scheme to simulate different complex flows. Investigation of moving boundaries in fluid flows is an important issue in the field of computational fluid dynamics. Regarding the characteristics of the LBE method, it can be a suitable means for the simulation of fluid flows containing moving boundaries. In the present thesis, we first evaluate different boundary conditions used in the LBE method. Bounce-Back boundary condition on lattice links is used in order to enforce no-slip boundary condition on the solid walls. Force evaluation is an important issue in the simulation of moving boundaries in fluid flows. The present work investigates two approaches for the force evaluation in the lattice Boltzmann equation, namely the momentum-exchange method and the stress-integration method on the surface of a body. In our investigation of several basic cases such as two-dimensional pressure driven channel flow and two-dimensional uniform flow past a column of cylinders, the advantages of the momentum exchange method such as its accuracy and ease of implication are studied. Finally, the “bounce back on links” scheme and “momentum exchange method” are used to simulate the motion of a 2-D cylinder in a channel flow with fixed walls and in a channel with impulsively moving walls. The motion of the cylinder is studied in two different frames of reference, i.e. a moving frame of reference which is located on the moving cylinder and a fixed frame of reference located on the channel walls. Comparing the forces on the cylinder in each frame of reference, the accuracy of the momentum exchange method as well as Galilean invariance of the lattice Boltzmann method is verified.