- In the present paper, the analogy between the Navier's equations of elasticity for compressible solids and the penalty function formulation of viscous incompressible fluids is utilized in a boundary element model to analyze problems of viscous incompressible flows in two dimensions. The equations of the penalty formulation of fluid flow are the same as those of the compressible elasticity with the Lam's constant equal to the penalty parameter, . The incompressibility condition is realized by setting the Poisson's ratio, , to 0.5. The fundamental solution of incompressible elasticity can be used, in conjunction with the boundary element method (BEM), to study the problem of viscous incompressible fluids. The resulting boundary element model does not suffer from numerical difficulties that the penalty finite element model is known to experience. Numerical results are presented to compare the penalty FEM and BEM solutions for a number of fluid problems. It is found that the boundary element model gives accurate solutions and it does not suffer from numerical difficulties. 1995.