Through a coordinate transformation approach, crystal orientation dependences of elastic and piezoelectric properties at room temperature have been investigated in a three-dimensional space for rhombohedral bismuth ferrite (BiFeO₃). Elastic constants (stiffnesses) , , c and piezoelectric constants , , along arbitrary orientations were obtained based on crystalline asymmetry characteristics of point group BiFeO₃. Parameters along specific orientations obtaining the largest values were presented. The = 213 × 10⁸ N/m² could be achieved in planes with ϕ = 0° and 90°. The = = 132.2 × 10⁸ N/m² could be achieved along directions at = 13° and = 77° inside three mirror planes, respectively. The = 27.6 × 10 C/N and the = 12.67 × 10 C/N could be both obtained along directions at = 69° inside mirror planes. The = 18 × 10 C/N could be obtained at = 0°, along the spontaneous polarization axis. By adopting optimal directions, the elastic and piezoelectric parameters of BiFeO₃ could be significantly enhanced which shows applications for the growth of BeFeO₃ films with preferred orientations and enhanced properties.