CONSIDERABLE progress has been made in the prediction of the unsteady aerodynamics of oscillating airfoils. These analyses are typically limited to inviscid potential flows, with the unsteady flow assumed to be a small perturbation to the mean flow and the Kutta condition imposed. By considering the airfoils to be zero-thickness flat plates at zero mean incidence, the steady and unsteady flowfields are uncoupled, with the steady flow being uniform and parallel. In this paper, an analysis is developed that models the unsteady aerodynamics of an harmonically oscillating flatplate airfoil, including the effects of mean flow incidence angle, in an incompressible laminar flow at moderate values of the Reynolds number. The unsteady viscous flow is assumed to be a small perturbation to the steady viscous flowfield. The nonuniform and nonlinear steady flowfield is described by the Navier-Stokes equations and is independent of the unsteady flow. The small-perturbation unsteady viscous flow is described by a system of linear partial differential equations that are coupled to the steady flowfield, thereby modeling the strong dependence of the unsteady aerodynamics on the steady flow. Solutions for both the steady and unsteady viscous flowfields are obtained by a locally analytical method in which the discrete algebraic equations representing the flowfield equations are obtained from analytical solutions in individual local grid elements. The locally analytical method for steady two-dimensional fluid flow and heat-transfer problems was initially developed by Chen et al. 1*2 They have shown that it has several advantages over finite-difference and finite-element methods, including being less dependent on grid size, with the system of algebraic equations relatively stable. Also, since the solution is analytical, it is differentiable and is a continuous function.