The inviscid method for unsteady flow, based on conformal mapping, developed earlier has been modified and applied to study various unsteady motions of two-dimensional airfoils. The two-dimensional form with a sharp trailing edge is transformed into a unit circle by two successive transformations. The change in circulation around the airfoil due to unsteadiness is modeled by discrete vortices which are shed from the trailing edge and allowed to move freely with local stream. The strength of these vortices is determined by the Kutta condition that, at each time step, the velocity be zero at trailing edge in the circle-plane. Calculations are made for a sinusoidal heaving motion, for an impulsively started airfoil and for an airfoil oscillating about a pivot axis. The analysis is performed in the relative frame of reference except for the motion due to pitching. A separate panel method is solved in the absolute frame to account for pitching part of the motion.