A solution in a double trigonometric series form is proposed for a forced vibration problem of a clamped orthotropic rectangular plate. With the increasing number of terms of the series, the solution satisfies more closely both the boundary condition and the governing equation. The accuracy of the solution is discussed numerically. As an example, the solution is applied to the iteration method for the analysis of the free vibration problem of a clamped orthotropic rectangular plate. Very accurate natural frequencies are obtained for typical plates.