The interaction between bone replacement bioceramic materials and the body will take place at the surface of the material. In the present ab initio study, we have investigated surfaces of biologically important alpha-tricalcium phosphate (TCP) and adsorption of biological species including a Ca atom, an H2O molecule, and a SiO2 fragment on the surfaces. The results show that all these species adsorb on the surfaces. The Ca atoms are strongly chemisorbed with newly created Ca-O bonds similar to those in alpha-TCP bulk in bond length; a water molecule is adsorbed and in some cases also dissociated on the surfaces with the dissociative adsorption, the predominant process; a SiO2 fragment initially linear, strongly interacted with two oxygens of different PO4 groups and eventually forms a tetrahedral SiO4-like species which might be a precursor of the silicate present in Si-TCP materials.