Elastic and hydrodynamic properties of biaxial nematics of D2 symmetry are theoretically studied. The treatment follows closely the classical formalism used for solids which is extended by inclusion of director fields. The resulting theory is a generalization of the well-established theory of uniaxial nematics. The elasticity and viscosity coefficients have similar physical meanings. The theory for incompressible biaxial nematics contains 12 relevant elastic constants and 12 viscosity coefficients. Three of the elastic constants can be assigned to twist deformations, six to bend deformations, and three to coupling between bend and twist. Nine of the viscosity coefficients can be determined in simple shear flow experiments. The remaining three describe the friction connected with the rotation of alignment axes.