Analytical/numerical matching (ANM) is a hybrid scheme combining a low-resolution global numerical solution with a high-resolution local solution to form a composite solution. ANM is applied to a harmonically oscillating body to calculate the radiated acoustic field and the associated fluid loading. The approach utilizes overlapping smoothed dipoles, and local corrections to calculate the dipole strength distribution along the surface of the body. A smoothing length scale is introduced that is larger than the smallest physical scale, and smaller than the largest physical scale. The global low-resolution solution is calculated numerically using smoothed dipole solutions to the wave equation, and converges quickly. Local corrections are done with high-resolution local analytical solutions. The global numerical solution is asymptotically matched to the local analytical solutions via a matching solution. The matching solution cancels the global solution in the near field, and cancels the local solution in the far field. The method is very robust, offering insensitivity to node location. ANM provides high-resolution calculations from low-resolution numerics with analytical corrections, while avoiding the usual subtleties involving singular integral equations, and their numerical implementation. The method is applied to calculate the radiated acoustic field and surface pressure of various flat plate configurations in two dimensions. An oscillating rigid flat plate, a forced elastic flat plate, plane-wave diffraction, and mechanical impedance calculations are addressed.