The Lees-Edwards description of bi-periodic boundary conditions hasbeen extended to the streamfunction and streamfunction-vorticityformulation in sliding bi-periodic frames. The required compatibilityconditions are formulated and uniqueness of the solution is shown.The model has been implemented in a spectral element method context todescribe bulk shear behavior far away from walls, where no simpleperiodic boundary conditions can be used. In the numerical model aLagrangian multiplier is introduced to couple the shearingboundaries. The proposed method has been validated for a mathematicaltest problem; convergence is shown and the influence of the order ofapproximation of the Lagrangian multiplier is studied. Finally,results are presented for drop coalescence across the boundaries ofthe bi-periodic frame.