A method of quantitative analysis of solids carrying drilling mud and removed from a drilling fluid circulating in a wellbore being drilled is described. The method comprises the steps of: sampling the removed solids, and analyzing the sample to determine the density of the solids and their weight fraction, drying a known weight of the sample to constant weight so as to obtain the solids in the form of dry solids, and analysis of the latter by an infrared spectroscopy technique. The concentration of the substances in the removed solids is then determined. The method can be applied to the control of the drilling operation by monitoring the quantity of products added to the drilling fluid, such as barite and polymers, or a product coming from the borehole wall or the underground formation being drilled. The invention also applies to the control of the working condition of the mud solids equipment.