A new three-dimensional fundamental solution to the Stokes flow was proposedby transforming the solid harmonic functions in Lamb' s solution into expressions in terms ofthe oblate spheroidal coordinates. These fundamental solutions are advantageous in treatingflows past an arbitrary number of arbitrarily positioned and oriented oblate spheroids. Theleast squares technique was adopted herein so that the convergence difficulties oftenencountered in solving three-dimensional problems were completely avoided. The examplesdemonstrate that present approach is highly accurate, consistently stable andcomputationally efficient.The oblate spheroid may be used to model a variety of particle shapes between acircular disk and a sphere. For the first time, the effect of various geometric factors on theforces and torques exerted on two oblate spheroids were systematically studied by using theproposed fundamental solutions. The generality of this approach was illustrated by twoproblems of three spheroids.