Compaction grouting is an improvement technique whose objective is to inject controlled grout masses to displace and compact the surrounding soil without fracturing it. The main application of this technique was for correction of settlement problems in structures, therefore, it was not specifically focused on soil improvement. This study presents some results on soil improvement by grout injection, in a deposit of dry or saturated loose sand, comparing numerical and analytical analyses. The numerical model consisted in a sequence of spherical cavity expansions of a grout bulb made by axisymmetric model with Plaxis 2D and tridimensional model with Plaxis 3D, both representing the soil mechanical behavior by either the Mohr-Coulomb or the HSM constitutive models, while the analytical consider the assumption of general shear failure of the soils overlying the injected masses in the form of a conical sheariThe efficiency of thaction grouting is evaluated mainly in terms of the increase in the ratio between initial and final radial stresses and shear modulus G with depth, as well as the increase of relative density Dr. The effective radius of compaction grouting extended to a radial distance close to 1,5m from the injection axis. The limiting pressures computed with axisymmetric model are all within the range of values reported in the literature and showed a significant difference with those obtained by the analytical solution. Another observation is that soil improvement analyzed by tridimensional model resulted greater than that obtained by the axisymmetric model due to the influence of the columns injected previously.