The elastic moduli of the vortex lattice in uniaxial strong type-II superconductors are calculated for magnetic inductions Hc1<<B<0.2Hc2 arbitrarily tilted with respect to the crystal axes. The derivation of the elastic moduli for the anisotropic situation is based on the mapping of the anisotropic problem to the corresponding isotropic situation. In performing this transformation we use the scaling rules connecting the anisotropic quantities with their known isotropic counterparts. The scaling approach is valid in the dispersive region which accounts for the major part of the Brillouin zone for fields B>>Hc1. The advantage of this method lies in its simplicity and in its general applicability. The resulting moduli agree with the elastic moduli derived previously by means of the traditional approach based on the expansion of the anisotropic London functional. In addition to the usual moduli, we obtain a new mixed shear-tilt modulus.