In this paper, the growth of intermetallic compound (IMC) layers is considered. After soldering, an IMC layer appears and establishes a mechanical contact between eutectic tin-silver solder bumps and Cu interconnects in microelectronic components. Intermetallics are relatively brittle in comparison with copper and tin. In addition, IMC formation is typically based on multi-component diffusion, which may include vacancy migration leading to Kirkendall voiding. Consequently, the rate of IMC growth has a strong implication on solder joint reliability. Experiments show that the intermetallic layers grow considerably when the structure is exposed to heat. Mechanical stresses may also affect intermetallic growth behavior. These stresses arise not only from external loadings but also from thermal mismatch of the materials constituting the joint, and from the mismatch produced by the change in shape and volume due to the chemical reactions of IMC formation. This explains why in this paper special attention is being paid to the influence of stresses on the kinetics of the IMC growth. We develop an approach that couples mechanics with the chemical reactions leading to the formation of IMC, based on the thermodynamically sound concept of the chemical affinity tensor, which was recently used in general statements and solutions of mechanochemistry problems. We start with a report of experimental findings regarding the IMC growth at the interface between copper pads and tin based solder alloys in different microchips during a high temperature storage test. Then we analyze the growth kinetics by means of a continuum model. By combining experiment, theory, and a comparison of experimental data and theoretical predictions we finally find the values of the diffusion coefficient and an estimate for the chemical reaction constant. A comparison with literature data is also performed.