This paper presents an analytical solution of one-dimensional free convection flow past an infinite vertical circular cylinder in a stratified fluid medium. The dimensionless unsteady coupled linear governing equations are solved by Laplace transform technique for the case when the Prandtl number is unity. Due to the effect of thermal stratification, the velocity, temperature, skin-friction and Nusselt number shows oscillatory behavior at smaller times and then reaches steady state at larger times, while this behavior is not seen in the absence of stratification.