method could be applied to evaluate the dyadic Green’s function and its derivatives in two-dimensional (2D) geometries. By using this method, the Casimir force between 2D objects could be simulated using much fewer unknowns and can be easily accelerated by fast-algorithms readily developed in computational electromagnetics. In this paper, we would extend the surface integral equation method for arbitrary three-dimensional (3D) geometries. The idea is similar to the last paper [20]: the Casimir force is expressed in terms of the dyadic Green’s function and its derivatives and they could be calculated from the integral equation by using different types of dipole point sources. The starting point of the stress tensor approach is that the net Casimir force acting on the surface S of an object is given by an surface integral of the mean stress tensor on it [14]: where T is the Maxwell stress tensor defined as in [18]. For an arbitrary 3D object, we define ˆ u and ˆ v as the tangent vector at the surface, and ˆ n as the normal direction of the surface. They satisfy the relationship ˆ u × ˆ v = ˆ n . If the object is a perfect conductor, the tangential electric field E$_{u}$ , E$_{v}$ and the normal magnetic field B$_{n}$ vanishes at the surface of the object. The stress tensor could be simplified as follows: Thus for perfect conductors, the Casimir force becomes a pressure on the surface. The average of the fluctuating electric and magnetic fields in the ground state is obtained from the fluctuation-dissipation theorem [19]: where the dyadic Green’s function is the same as that defined in classical electromagnetics to relate the current to the field in an arbitrary geometry [20]. In 3D structures, the field components and the dyadic Green’s function satisfy the fol- F = ∮$_{S}$ 〈 T ( r $^{′}$) 〉 · d s ′ (1) T$_{nn}$ ( r ) = 1 2 ϵ 0 E 2 $_{n}$( r ) − 1 2 µ 0 B 2 $_{u}$( r ) − 1 2 µ 0 B 2 $_{v}$( r ) (2) T$_{un}$ ( r ) = T$_{vn}$ ( r ) = 0 (3) 〈 0 | ˆ E$_{i}$ ( r , t ) ˆ E$_{j}$ ( r $^{′}$, t ) | 0 〉 = ℏ π Im ∫ ∞ 0 ω $^{2}$G$_{ij}$ ( r , r $^{′}$, ω ) dω (4) 〈 0 | ˆ B$_{i}$ ( r , t ) ˆ B$_{j}$ ( r $^{′}$, t ) | 0 〉 = ℏ π Im ∫ ∞ 0 ( ∇× )$_{il}$( ∇ $^{′}$× )$_{jm}$ G$_{lm}$ ( r , r $^{′}$, ω ) dω (5) 4