In modern microelectronic packages (considered here as a mesoscale), the size of microstructural features of an alloy is compatible with the scale of an entire element that can contain only one or a few grains. In this case, the mechanical behaviour of the element deviates from isotropic/homogenous character at the macroscopic scale of a bulk specimen, comprising a large number of randomly oriented grains. Generally, a crystal-plasticity model, which is based on dislocation sliding in certain slip systems, is applied to describe a local lattice-induced anisotropic behaviour. However, even at a room temperature, the movement of dislocations is not a single mechanism of the inelastic behaviour of eutectic SnAgCu solder due to its low melting point. Under a low-magnitude loading condition, creep also has an effect due to a movement of vacancies. At high temperatures, this creep can become a dominant mechanism for the inelastic behaviour, diminishing the role of the crystal-plasticity model. This paper accounts for the creep component of deformation and unites it with the traditional crystal-plasticity model. In addition, deformation due to thermal expansion is introduced into the constitutive equation to capture the major mechanisms of the mechanical behaviour of a SnAgCu solder micro-joint used in electronics.