This paper presents the force coefficients (added mass and damping) for a circular cylinder oscillating horizontally in a uniformly stratified fluid of limited depth and in a continuously stratified fluid with a smooth pycnocline. The frequency-dependent added mass and damping are evaluated from Fourier transforms of the experimental records of impulse response functions. The stratification is shown to have a strong effect on the fluid–body interaction. It is found that, when the characteristic vertical extent of stratification (depth of uniformly stratified fluid or pycnocline thickness) decreases, the power radiated with internal waves is reduced and the maximum of the frequency spectrum of wave power shifts toward lower frequency. The results of experiments are compared with available theoretical predictions.