The lattice Boltzmann method offers an alternative framework compared to the Navier-Stokes simulations. However, the applicability of this method to simulate moving boundary problems has not received sufficient attention. In this work, different treatments of the no-slip condition of lattice Boltzmann method for the moving boundary problem of rigid and flexible wings flapping in a fluid have been analyzed. Schemes based on interpolation have been considered in the scope of flapping and plunging wing simulations to analyze the accuracy of the solution near the moving boundary. It is shown that interpolation resolves the exact location of the wall accurately when the distance from the nearest lattice, Δ≠ 1/2, unlike the halfway bounceback method. Flow past a vertically oscillating plate at Re= 100 with two different amplitudes is simulated. The presence of large fluctuations in forces, due to different levels of accuracy of pressure and velocity, at the time instant when an oscillating plate crosses into the adjoining lattice is shown. For a three-dimensional zero-thickness flat plate undergoing hovering motion with delayed rotation, interpolation schemes show better agreement with Navier-Stokes solution as compared to the halfway bounceback method. The flow field computed using interpolation indicates a continuous variation of pressure and vorticity near the surface of the wing. Lattice Boltzmann simulation of a finite-thickness flat plate is also shown to be in good agreement with the Navier-Stokes solution. Preliminary results of a two-link flexible wing model undergoing pitching and plunging motion are also presented. Through simulations using the flexible-particle model, good agreement with the force and deflection angle recorded in earlier experiments is reported.