We employ classical molecular dynamics to calculate elastic properties and to model the nucleation and propagation of deformation twins in calcite, both as a pure crystal and with magnesium and aspartate inclusions. The twinning is induced by applying uniaxial strain to the crystal and relaxing all stress components except the uniaxial component. A detailed analysis of the atomistic processes reveal that the twinning mechanism involves small displacements of the Ca ions and cooperative rotations of the CO₃ ions. The volume of the twinned region expands under increased uniaxial strain via the propagation of steps along the twin boundaries. The energy cost of the twin boundaries is compensated by the reduced hydrostatic stress and strain energy. The presence of biogenic impurities is shown to decrease the strain required to induce twin formation in calcite and, thus, the yield stress. This increased propensity for twinning provides a possible explanation for the increased hardness and penetration resistance observed experimentally in biominerals.