The joinability of materials that show significant difference in their physical and chemical properties is a function directly proportional to the absolute number of Gibbs free energy negative value and to the values of the diffusion coefficients of the ions or atoms of couple of materials under joining, and inversely proportional to the difference of their thermal expansion coefficients. The paper presents the results of the research on joining ceramic materials (Si3N4, AIN and Al2O3) with the application of compensation interlayers, layers consisting of the functional gradient materials (FGM) and specially designed composite fillers of AgCuTi - carbon fibre. The analyses of the internal stresses performed by the finite element method enable us to determine the quantities of these stresses and their distribution in the joined materials, which allows us to design the shape of a joint and the possible interlayers.