The vibrational frequencies of a 24-layer CsCl (001) slab have been calculated with an eleven-parameter shell model. Without surface relaxation, the results exhibit an instability in the form of a pair of imaginary-frequency Rayleigh modes for wave vectors over most of the surface Brillouin zone. To investigate the effects of relaxation on this dynamic instability, two kinds of relaxation have been used; (i) an inward relaxation of the two outermost planes, and (ii) an expansion of the entire slab in the z-direction (i.e. normal to the surfaces), followed by an inward relaxation of the two outermost planes. In the first case, the imaginary frequencies are removed for most wave vectors except for those very close to the zone center. In the second case, the imaginary frequencies are removed for all wave vectors. Due to the occurrence of two different surfaces of the slab, one containing only Cs + ions, the other only Cl − ions, two classes of surface modes are found: one with the vibrational amplitudes decreasing from the top layer to the bottom layer, the other vice versa. Longitudinal and transverse optical, and transverse accoustical surface modes are found in both classes. The frequencies of these surface modes are strongly dependent on the surface relaxations.