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We develop a finite-element analysis (FEA) model to describe transient and static operation of gas-exchange valves. Such valves, directly controlled by solenoids, are a promising method for enhancing automotive engine efficiency. The FEA model is validated by experimental testing on an actual automotive prototype valve. We show that a nonlinear lumped-parameter model that uses FEA results also closely matches experimental data. The lumped-parameter model is suitable for optimization of design and can be readily used for closed-loop simulation. We present a simplified lumped-parameter model to facilitate controller design. Finally, we compare a dynamic open-loop simulation with experimental results.