The use of compactly supported wavelet functions has become increasingly popular in the development of numerical solutions for differential equations. Daubechies wavelets have been successfully used as base functions in several schemes like the Galerkin Method. Meanwhile, Deslauriers and Dubuc developed a new wavelet family with interpolating characteristics called Interpolets. One important contribution presented in this work is the formulation of Finite Elements based in Daubechies wavelets and Deslauriers-Dubuc interpolets. Dynamic problems like wave propagation and structural stability problems were used as examples for the validation of the Finite Elements. The Wavelet-Galerkin Method has then been adapted for the direct solution of differential equations in a meshless formulation. This approach enables the use of a multiresolution analysis. Several examples with discontinuities and nonlinearities were studied successfully.