In this paper, steady incompressible flow patterns inside two-dimensional triangle, trapezoidal, semi-circular and arc-square cavities with moving boundaries are studied via lattice Boltzmann method. The effects of geometry of the cavities on flow pattern are also discussed. The effects of Reynolds number on the flow patterns in triangular, semi-circular and arc-square cavities are studied. Also, for arc-square cavity, it can be observed that by changing the size of top and bottom walls which means a change in the size of cut arcs from the circular, different flow patterns are formed. The influences of the side angles at constant Reynolds number on the flow patterns in the trapezoidal cavities are investigated. It is found out that the vortex near the bottom wall of trapezoidal cavity breaks up into two smaller vortices as side angles increase. The obtained results of the lattice Boltzmann method and the presented boundary condition are compared with those presented in the literature. It can be seen that the lattice Boltzmann method is a suitable method for flow simulation in the mentioned cavities.