A generalized hydrodynamical model has been used to study low frequency modes in a strongly coupled, cold, magnetized dusty plasma. Such plasmas exhibit elastic properties due to strong correlations among dust particles and the tensile stresses impar
ted by the magnetic field. It has been shown that longitudinal compressional Alfven modes and elasticity modified transverse shear mode exist in such a medium. The features of these collective modes are established and discussed.
