The present invention refers to a method for eliminating silicon or silicon compounds that are contained in alumina based materials without destroying such alumina based materials allowing for their reutilization, its main application is being the regeneration of alumina based catalyst contaminated with silicon, which are used in hydro-treating processes in the oil industry for sulfur elimination and silicon removal from process streams. It is important to note that the procedures and/or conventional methods known so far for the elimination and removal of silicon contained in alumina based materials, use inorganic acids or their mixture in a digestion process which modifies the properties of alumina and of any other element contained in the material, thus destroying the alumina and disabling their reutilization. The non-destructive method of the present invention is characterized by the fact that an extraction agent depolymerize the silicon compounds deposited in alumina based materials, with no modification of the properties of the alumina based material and with no substantial modification of other materials o or on the metal content present in the alumina based material. The extraction agent used is an alcohol, preferably a polyol and more preferably glycerol, which is available needless of high grade of purity for its use. The silicon contained in alumina based materials, in which the non-destructive method of the present invention is used, is preferably found in inorganic structures such as oxide or silanol: Si—(OX)4(X═Al, H, Si) and/or as organosilanes structures: (OX)3—Si—CH3 and/or (CH3)2—Si—(OX)2(X═H, Si), both are depolymerized when this removal method is used.