This paper investigates the generation of linear baroclinic Rossby waves by a steady zonal current, which either translates at a constant speed or oscillates sinusoidally in latitudinal position. An analytical solution is found for forcing by a steadily moving current, and this confirms the numerical results. A numerical model, in a reduced gravity ocean, produces solutions for oscillating current forcing. All the results indicate a strong relationship between the wave crest orientation (and phase speed direction) of the response, and the speed of motion of the current. This is elucidated by reference to the work of Lighthill (1967) on moving forcing effects.