This thesis presents the results obtained so far in an investigation concerning viscous effects in incompressible flows over airfoils. These effects are taken into account by assuming the existence of a boundary layer which interacts with an external inviscid flow. Numerical methods for solving the inviscid and boundary-layer flows are briefly described. The main objective of the investigation is the development of an interaction technique between both regions of flow. The method chosen for the interaction is the so-called semi-inverse procedure. This procedure is derived from a perturbation analysis of the linearized versions of the governing equations. The resulting method is subjected to a stability analysis, which shows that it will break down when used in conjunction with separated-flow boundary-layer solvers. The semi-inverse procedure is tested on several airfoils, using an attached-flow boundary-layer solver. Numerical results show that the method is sufficiently accurate for engineering purposes in the low-to-medium range of angles of attack, but its applicability is questionable when there is a large separation region. Finally, recommendations are made regarding future work to overcome the limitations of the present technique. / Master of Science