This invention provides a material for vibration damping, said material comprising a composite, said composite comprising a cement matrix, and exfoliated graphite that is distributed in said composite. Said cement is preferably hydraulic cement containing calcium silicate. Said exfoliated graphite exhibits a morphology that enables the physical units of exfoliated graphite to connect mechanically. The proportion of exfoliated graphite in the composite is high enough for the exfoliated graphite to connect mechanically in the presence of cement. The proportion of cement in the composite is high enough for the cement to form a continuous matrix in the composite. This invention also provides a material for vibration damping, said material comprising a composite, said composite comprising a continuous cement matrix and a graphite network, said network being mechanically connected. In addition, this invention provides a method for making a material for vibration damping, said method comprising compressing a mixture of exfoliated graphite and cement particles at a pressure that is sufficient to cause the exfoliated graphite to bind the cement particles through mechanical connection between the physical units of exfoliated graphite, and curing the cement in the presence of water that is adequate for the cement particles to bond cementitiously to one another.