We have derived a potential model for fluorapatite Ca₁₀(PO₄)₆F₂, fitted to structure, elastic constants and vibrational frequencies of the phosphate groups, which is compatible with existing calcite and fluorite potential models. We then modelled the structure and stabilities of the dry and hydrated {0001}, {100}, {101}, {110}, {103} and {111} surfaces, which calculations confirmed the experimental dominance of the {0001} surface, which is prominently expressed in the calculated thermodynamic morphologies. The dehydrated morphology further shows the experimental {111} twinning plane, while the {100} cleavage plane is expressed in the hydrated morphology. Molecular adsorption of water has a stabilising effect on all six surfaces, where the surfaces generally show Langmuir behaviour and the calculated hydration energies indicate physisorption (73–88 kJ mol⁻¹). The chains of fluoride ions surrounded by hexagonal calcium channels can become distorted in two major ways: either by a shortening/lengthening of the F–F distances, when the channel is perpendicular to the surface, or by distortion of the Ca–F bonds when the channel is parallel to the surface. Both distortions occur when the channel runs at an angle to the surface. Other relaxations include compression of the calcium sub-lattice and rotation of surface phosphate groups.