1. In the present paper, a numerical method of getting differential coefficients of high order is presented. A continuously differentable function ƒ is approximated by the linear combination of pyramid-shaped base function { Φi } and coefficients { αi } as ƒ≈∑ iαiΦi Then, n th derivated function ∂nƒ/∂xk, …∂xl is also approximated with { Φi } and other coefficients { α∂xk, …∂xli } Using theory of distribution, coefficients { α∂xk, …∂xli } is expressed in terms of { αi } After all, n th derivated function is approximated by following form. ∂n/∂xk, …∂xl ƒ≈∑ iα∂xk, …∂xliΦi =∑ ijαjN∂xk, …∂xlijΦi α ∂xk, …∂xli =∑ jN∂xk, …∂xlijαj 2. The method is applicated for forced vibration of a beam. Partial differential equations of beam vibration contain two differentials of 2nd order and 4th order ; ∂ 2/ ∂t 2 and ∂ 4/ ∂x 4. Though it is said to be difficult to build a space-time element applicable for such problem, it is quite easy to apply a space-time element for FEM analysis using the present method.