This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non-moving mean wall positions by assuming the airfoil being thin and undergoing small deformation, but the mean angle of attack of the body can still be large and we use the full nonlinear Euler equation in the field for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body-fitted grids and thus can be easily deployed in any fluid-structure interaction problem involving relatively small deformation of a thin body. We use the first-order wall boundary conditions in solving the full Euler equation. Unsteady transonic flow is calculated about an oscillating NACA 0012 airfoil at free stream Mach number M∞=0.755, mean angle of attack αm=0.016, amplitude of pitching oscillation α0=2.51, reduced frequency κ=0.081 4. The computed results, including surface pressure distribution, instantaneous lift and moment coefficients are compared with known experimental data. It is shown that the first-order boundary conditions are satisfactory for airfoils of typical thicknesses with small deformation for unsteady calculations.