We use computer simulations to determine the dominant unstable modes of stellar discs having the surface density distribution of Toomre's (1963) model 1 and large random motions in the plane. Particles in the models have their initial coordinates chosen from distribution functions to ensure that the configurations would, in the limit of infinitely many particles, be stationary solutions of the Vlasov and Poisson equations. The 40,000 particles in our simulations are constrained to move on a plane and we use a polar grid based Fourier method to determine the force field (Sellwood 1982). The surface density is smoothly tapered to zero at six scale lengths and the softening length is 1/30th of the outer radius of the disc.