The differences in the coefficient of thermal expansion (CTE) between the chip and the FR-4 board generate the shear strains and the bending moment in the solder joint. It seems to be a main cause of failure in the solder joint when the chip and the FR-4 board are heated repeatedly. Thus, the fatigue loading induced by thermal cycling is a major concern in the reliability of the solder joint. The magnitude of shear strain and the final failure are known to be influenced by varying boundary conditions such as the difference of CTE, the height of solder, the distance of the solder joint from the neutral point (DNP) and the temperature variation. In this paper, the effects of boundary conditions on the failure probability of the solder joint are studied by using the failure probability models such as the First Order Reliability Method (FORM) and the Monte Carlo Simulation (MCS). Furthermore, the stiffness of the solder joint is considered to investigate the influence at the failure probability.