This paper is devoted to a new algorithm to compute the local and overall response of a composite. The local elastic problem is discretized by a Galerkin-wavelet method. Details are given to compute the terms of the matrix and of the right hand side. The local solution is selected by a viscosity method. The solution with average equal to zero is chosen. Due to the form of the wavelet bases, the macroscopic coefficients are computed directly from the wavelet coefficients of the solution. Numerical examples are presented. Comparisons are made with analytic solutions and with finite element computations.