The classical theory of elasticity describing three- and lower-dimensional systems is generalized to higher-dimensional spaces. The elastic properties of quasicrystals can be derived from this theory, appropriately. The practical application is given to pentagonal, octagonal, dodecagonal, and icosahedral quasicrystals. The explicit form is obtained for all elastic equations including Hooke's law, equilibrium equation, etc., in all the cases mentioned above.