Steering torque feedback plays an important role in driver-vehicle dynamics. Existing mathematical driver models with steering torque feedback are reviewed. It is argued that a new linear parametric driver-steering-vehicle model is required to provide greater insight to subjective assessment of steering torque feedback. The proposed new model incorporates: neuromuscular dynamics; proprioceptive (muscle stretch) and visual sensory dynamics; steering torque perception via efference copy; process and measurement noise; state estimator; and an internal predictive model of the plant. A series of path-following experiments with thirteen test subjects is performed on a fixed-base driving simulator. Each test subject performed three different trials in the ‘on-centre’ regime of operation. A Box-Jenkins model accounted for 90% of the variance of the measured handwheel angle time series averaged over the thirteen test subjects (VAF). The unknown parameter values of the new parametric model were identified from the driving simulator data. The prediction accuracy approached the upper bound given by the Box-Jenkins model. Process noise was found to be linearly dependent on muscle activation torque, and this signal-dependent behaviour was also present in the measurement noise. The model was re-identified using signal to noise ratios as parameters. The VAF was 86.6%, close to that of the Box-Jenkins model, and the identified parameter values are physically plausible, giving confidence that the model is suitable for further work on understanding steering torque feedback.