This paper presents the mathematical details of the formulation for the sensitivity derivatives for the structural dynamic, aeroelastic stability, and response characteristics of a rotor blade in hover and forward flight. The formulation is denoted by the term semi-analytical approach, because certain derivatives are evaluated by a finite difference scheme. Using this formulation, sensitivity derivatives for structural dynamic and aeroelastic stability characteristics were evaluated for a composite rotor blade. Useful conclusions regarding the relative merits of the semi-analytical approach, when compared to a pure finite difference approach, are obtained. In addition, influence of ply orientation angles on the vibratory hub loads in forward flight is also considered. © 1994.