In this paper, a nonlocal computational method is proposed to construct a mesoscopic (coars-grained) model of linear elastic heterogeneous materials in the case of nonseparated scales. The framework, introduced in our previous paper (Yvonnet and Bonnet, 2014) extends the classical homogenization framework by using low-pass filters operators instead of averaging operators, and Green's nonlocal functions instead of localization operators. In the present work, we introduce a filtering procedure based on least-square polynomial approximation to avoid the numerical drawbacks of Gaussian filters in finite domains. The complete associated homogenization scheme is described, as well aa a numerical procedure based on finite elements to compute the different homogenized operators from a unit cell. The methodology is validated by analyzing both local and mesoscopic mechanical fields in structures where heterogeneities are of comparable size with respect to the loading characteristic fluctuation wavelength.