In order to predict properties of a formation in a near-wellbore area exposed to a drilling mud rheological properties of the drilling mud, of a filtrate of the drilling mud and of a reservoir fluid are determined. Properties of an external mudcake, porosity and permeability of the core sample are determined. A mathematical model of the external mudcake is created. The drilling mud is injected through a core sample and dynamics of pressure drop across the sample and dynamics of a flow rate of a liquid leaving the sample are determined. Using an X-ray micro Computed Tomography a profile of concentration of particles of the drilling mud penetrated into the sample is determined. A mathematical model is developed for the internal mudcake to describe dynamics of changes in concentration of the particles of the drilling mud in a pore space of the core sample. A coupled mathematical model of the internal and the external mudcakes is created and parameters of the mathematical model of the internal mudcake are determined providing matching of simulation results to the experimental data on injection the drilling mud through the core sample and to the concentration profile of the particles of the drilling mud.