Abstract A method of design sensitivity analysis for a failure probability is presented and formulas are derived, such that a gradient-based optimization technique can be applied for a general reliability-based optimal design formulation. It is based on using an advanced first order second moment (AFOSM) method in evaluating the probability. The resulting sensitivity coefficient contains only first order derivatives. Hence, it is very suitable for numerical implementation. The method is illustrated by several examples which include cases with state equations from a finite element method. A frame optimal design is also presented to demonstrate the method of solution for the reliability-based optimal design.