We use numerical simulations to investigate excitation of topographic vorticity waves (TVWs) along the Antarctic continental slope by outflows of dense shelf water through troughs. Idealized models show that wave frequency depends on the amount of stretching in the ambient fluid over the outflow and on background along-slope mean flow. Frequency is higher for steeper bottom slope, larger outflow density anomaly, and stronger westward mean flow. For weak stratification and weak westward along-slope flows typical of the Antarctic slope, wave energy propagates eastward, in the opposite direction from phase velocity. Our results are consistent with recent observations of TVWs in the southern Weddell Sea. In a realistic simulation of the Ross Sea, TVW properties are modulated on seasonal and shorter time scales as background ocean state varies. We expect these waves to affect mixing, cross-slope exchanges, and sea ice concentration in the vicinity of sources of dense water outflows.