The authors present an efficient pseudospectral method for incompressible flow simulations in two-dimensional geometries involving periodicity in one direction and significant surface deformations. A pseudoconformal map is used to map the flow domain into a rectangle, thereby establishing an orthogonal curvilinear coordinate system. Time integration is performed by a second-order mixed explicit/implicit scheme. The continuity equation is satisfied by the solution of Poisson equation for the pressure and by the use of influence matrix techniques. The authors employ a highly efficient iterative solver with a spectrally preconditioned biconjugate gradient algorithm. Numerical results are presented for two-dimensional steady, oscillatory, and peristaltic flows within an undulating channel.