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An alternate approach to speech synthesis based on numerical solution of Navier-Stokes (NS) and Reynolds-Averaged-Navier-Stokes (RANS) equations is described. Unlike the traditional methods based on linear acoustic theory, the NS and RANS formulations are not limited by the assumptions of linearity, negligible viscous effects, and plane wave propagation. In the present formulation, the Navier-Stokes equations are discretized and solved using a finite difference method. Initial applications involve 2-D simulations of flow through ideal channels (straight or curved tubes) with rigid walls and constant boundary conditions (constant flow velocity at inlet, zero pressure at outlet). As expected for simple geometries, the resonance frequencies correspond to those predicted by linear acoustics. It is also shown that for curved tubes, there is an effect of curvature on frequencies above 5 kHz. In another application, the formulation is applied to the geometry of the three cardinal vowels. Periodic inflow boundary conditions are also used (a train of short pulses to represent vocal cord excitation). Synthetic speech sounds of encouraging quality are obtained for the three vowels.