In this study, the finite element analysis is chosen to investigate the thermo-mechanical properties of an indium joint exposed to low-temperature cycling. Based on the experimental data, the computational model is built, and the material model of indium is proposed for different joint thickness. The obtained results demonstrate that the outmost corner of the interface between the small indium joint and copper substrate is the weak site, while the large indium joint is characterized by a perfectly elastic core surrounded by uniformly plastic deformation during low-temperature cycling. With the proposed material model, the package-indium bump bonding with sensor and readout, used in the photon counting pixel detector Medipix 3, was studied under conditions of low-temperature cycling. The study provides an insight into the response of joints to thermal fatigue in indium joints during low-temperature cycling.