Lead-free tin-based solder joints often have a single-grained structure with random orientation and highly anisotropic properties. These alloys are typically stiffer than lead-based solders, hence transfer more stress to printed circuit boards (PCBs) during thermal cycling. This may lead to cracking of the PCB laminate close to the solder joints, which could increase the PCB flexibility, alleviate strain on the solder joints, and thereby enhance the solder fatigue life. If this happens during accelerated thermal cycling it may result in overestimating the lifetime of solder joints in field conditions. In this study, the grain structure of SAC305 solder joints connecting ceramic resistors to PCBs was studied using polarized light microscopy and was found to be mostly single-grained. After thermal cycling, cracks were observed in the PCB under the solder joints. These cracks were likely formed at the early stages of thermal cycling prior to damage initiation in the solder. A finite element model incorporating temperature-dependant anisotropic thermal and mechanical properties of single-grained solder joints is developed to study these observations in detail. The model is able to predict the location of damage initiation in the PCB and the solder joints of ceramic resistors with reasonable accuracy. It also shows that the PCB cracks of even very small lengths may significantly reduce accumulated creep strain and creep work in the solder joints. The proposed model is also able to evaluate the influence of solder anisotropy on damage evolution in the neighbouring (opposite) solder joints of a ceramic resistor.