The effect of thermal radiation absorption on an unsteady free convective flow past a vertical plate is studied in the presence of a magnetic field and constant wall heat flux. Boundary layer equations are derived, and the resulting approximate nonlinear ordinary differential equations are solved analytically using asymptotic technique. A parametric study of all parameters involved is conducted, and a representative set of numerical results for the velocity and temperature profiles as well as the skin-friction parameter are illustrated graphically to show typical trends of the solutions.