A device for estimating a friction coefficient between a road surface and an automotive tire through determination of a steering torque during a steering maneuver of a slow-rolling or stationary vehicle includes a computer configured for constructing a brush model for a description of the steering torque across a contact patch between the tire and road surface. The steering torque is a torque acting on a steering axis required to overcome resistance to tire twisting on the road surface at a wheel velocity and a steering rate. The steering torque depends on a tire brush vertical load distribution and relative motion of tire brushes and the road surface. The device further includes sensors for measuring the wheel velocity and the steering rate and mechanism for measurements or estimation of the steering torque. The friction coefficient is estimated based on the measurements or estimation of the steering torque and the brush model.