A reliability-based shape optimization is formulated using the advanced first order second moment (AFOSM) method for the evaluation of failure probability, and the boundary element method (BEM) for the calculation of stress and evaluation of shape design sensitivity. A fully analytical approach is adopted for the design sensitivity analysis where the boundary intergral equation (BIE) is implicitly differentiated. In order to illustrate the application of the present methodology two examples are taken. One is a plate with a central hole. Loads and yield stress are taken as random parameters with normal distribution. The other is a fillet problem where load, yield stress and Poisson's ratio are taken randomly. The results are compared with deterministic cases and their practicability is shown.