In this paper, we have studied the dependencies of group velocity and damping of magnetoelastic surface waves on the frequency at various external magnetic fields and propagation angles. The group velocity spikes occur at frequencies at which the damping peaks of the surface wave are detected. The behavior of a surface magnetoelastic wave in the vicinity of the orientational phase transition was also investigated. At the phase transition point, the group velocity changes by 1%. Dependences of the damping along the surface at various propagation angles point out on the nonreciprocal nature of the wave. All dependencies in this work were obtained using computer modeling. The parameters of the ferromagnet are taken typical for yttrium-iron garnet.