The near wake of a circular cylinder in linearly stratified flows of finite depth was experimentally investigated by means of flow visualization and measurements of vortex shedding frequencies, at Reynolds numbers 3.5x10^3-1.2x 10^4 and stratification parameters k_d 0-2.0. The non-dimensional parameter k_d is defined as k_d=Nd/U, where N is the Brunt-Väisälä frequency, d, the diameter of the cylinder, and U, the approaching flow velocity. The study demonstrates that as k_d increases from zero, the vortex shedding from a circular cylinder progressively strengthens, while the Strouhal number gradually becomes lower than that for homogeneous flow. This phenomenon can be explained by the effect of the increasingly stable stratification which enhances the two-dimensionality of the near-wake flow of the circular cylinder; the enhanced two-dimensionality of the flow strengthens the roll-up of the separated shear layer. Above a certain value of k_d, however, vortex formation and shedding are strongly suppressed and the Strouhal number rises sharply. This observation is attributable to the development of stationary lee waves downstream of the circular cylinder because the lee waves strongly suppress vertical fluid motions.