In this paper, an approach is proposed for taking calculations of high orde
r differentials of scaling functions in wavelet theory in order to apply th
e wavelet Galerkin FEM to numerical analysis of those boundary-value proble
ms with order higher than 2. After that, it is realized that the wavelet Ga
lerkin FEM is used to solve mechanical problems such as bending of beams an
d plates. The numerical results show that this method has good precision.