Compression, tension and torsion tests were designed and completed successfully on a brushite and a precipitated hydroxyapatite cement in moist condition. Elastic and strength properties were measured for these three loading cases. For each cement, the full set of strength data was fitted to an isotropic Tsai-Wu criterion and the associated coefficients identified. Since the compressive Young's moduli were about 10% larger than the tensile moduli, the full set of elastic data of each cement was fitted to a conewise linear elastic model. Hysteresis of the stress-strain curves was also observed, indicating dissipation mechanisms within these cement microstructures. A comparison of the measured mechanical properties with human cancellous bone confirmed the indication of brushite as a bone filling material and the potential of the hydroxyapatite cement as a structural biomaterial.