||The formation of cold core filaments on an idealized continental shelf is investigated using a numerical model to simulate the ocean's response to surface cooling. A horizontal density gradient forms because of uneven buoyancy loss due to the sloping bottom, and this gradient induces an alongshelf current in thermal wind balance, that in time becomes unstable. As the instabilities grow, filaments, and later eddies, are generated so that dense water near the coast is mixed offshore. Scaling arguments of the filament wavelength indicate that the current is baroclinically unstable, and an analytical model of the frontal expansion with time is in very good agreement with the simulations. This study was inspired by satellite observations of sea surface temperature on the West Florida Shelf during the winter months, in which it is clearly seen that cold core filaments extend from a thermal front. Numerical experiments are therefore designed to allow for reliable comparisons with conditions in this region.