This paper presents a future development of wavelet Boundary Element Method using non-orthogonal spline wavelet for 2-D linear lasticity. In this work, Non-orthogonal spline wavelets are used as basis for boundary elements method. This kind of wavelets has been proposed by authors. The use of the wavelets as basis function is accepted as a fast solution comparable to the fast multiple BEM. Using wavelet as basis function, many coefficients of the equations (matrix coefficients), which are defined as the integrals including the fundamental solutions and the basis on boundary, have small values owing to the vanishing moment property of wavelets. The compression algorithm is performed so that the amount of storage (and computational work) is minimized without reducing the accuracy of boundary equation solution. To avoid the unnecessary integration concerning the truncated entries of matrix coefficients, a priori estimation of the matrix entries is introduced. The matrix compression for the proposed wavelet BEM enables us to generate a sparse matrix. The matrix truncation schemes are applied using the Schneider level-dependent method and the Beylkin-type compression and the results are compared.As a result, the matrix compression rate using the Beylkin-type is greater than or similar to that using Schneider’s level-dependent scheme. Numerical results presents in this paper show good agreement with analytical solutions.