The orientational elasticity of the uniaxial and the biaxial nematic phases is deduced earlier. For bent–core molecules with hardcore interaction, we examine how the molecular shape affects the elastic constants of these phases. The calculation is built on a tensor model based on the Onsager theory. The elastic constants are expressed by the coefficients in the tensor model, and these coefficients are derived from molecular parameters. We calculate the elastic constants of bent–core molecules as functions of the bending angle, concentration and thickness. We also examine the elastic constants of star molecules, where we focus on the effect of the extra arm.