The viscosity of a dilute suspension of charged rigid particles exceeds that of a suspension of identical, but uncharged particles, and this is called the primary electroviscous effect. This excess viscosity arises as a result of the distortion of the ion atmosphere surrounding the polyion due to the fluid shear field in which it is placed. Consequently, any theory of the primary electroviscous effect must account for this distortion. Booth(Proc. Roy. Sec. (London) 1950, 203A, 533) and later Sherwood (J. Fluid Mech. 1980, 101, 609) achieved this for a spherical polyion of uniform equilibrium surface potential by solving the coupled (low Reynold＇s number) Navier-Stokes, Poisson, and ion transport equations. The primary objective of the present work is to extend this approach to rigid model polyions of arbitrary shape and charge distribution. The coupled transport equations are solved by an iterative boundary element (BE) procedure applied previously to the closely related problem of electrophoresis (Allison, S. A. Macromolecules 1996, 29, 7391). In test cases on spheres containing single central charges, the BE results are found to be in very good agreement with Sherwood. The BE approach is then applied to spherical polyions containing noncentrosymmetric charge distributions as well as short (20-40 base pair) DNA models in the monovalent salt range 0.005-0.6 M. For the DNA fragments, the primary electroviscous effect ranges from about 2% to 30% (40 bp) or 45% (20bp) as the KCl concentration is reduced from 0.6 to 0.005 M, respectively. Substantially larger effects are predicted if the monovalent salt is Tris-acetate, and this is due primarily to the lower mobility of the Tris counterion relative to KC. A secondary objective is to make contact between the BE approach and "bead methods", which have been successfully used in modeling the viscosity of rigid, but uncharged macromolecules of arbitrary shape.