A procedure for second-order computational homogenization of layered rock masses is derived in order to describe the effect of the material heterogeneities and to include scale effects on the shear wave propagation. The homogenization procedure is based on an appropriate representation of the micro-displacement field in the unit cell which is assumed as the superposition of a local macroscopic displacement field and an unknown micro-fluctuation field accounting for the effects of the heterogeneities. This second contribution is represented as the superposition of two unknown functions that guarantee the continuity of the micro-displacement field. Shear dispersive waves are obtained in a layered rock mass and in a damaged layered rock mass with periodic discontinuity planes in the stiffer layer. The obtained results differ from the corresponding ones resulting from standard Cauchy homogenization.