Rate-and-state-friction is an empirical approach to the behavior of a frictional surface. Here, we use a model of a liquid crystal fluid in a channel between two planes to model frictional sliding. Liquid crystals are extensively studied and have applications to a wide variety of engineered systems, including systems that rapidly switch between states. The liquid crystal is characterized by a directional field, d(z,t) where z is the distance from the fixed plane and t is time. The viscosity of the liquid is a function of the director field, with a minimum viscosity ν0 corresponding to the viscosity if the director field pointed in the horizontal direction, and a maximum ν_1 corresponding to the viscosity when the director field is pointing in the vertical direction. A third parameter λ is the relaxation coefficient of the director field. The viscosity is given by ν=α(θ)ν_1+(1-α(θ))ν0 where θ is the angle of the director field d with respect to vertical. The choice of the viscosity function α(θ) determines the behavior of the system. In response to sliding of the moving plate, the fluid undergoes a rapid increase in resistance followed by relaxation. The directional field is deflected from vertical and strain is localized within the channel. The directional field plays a role analogous to the state variable in rate and state friction. Reducing the relaxation coefficient of the director field λ produces a sharper increase in the traction change with velocity, but too small λ can cause instability in the simulation. Reducing ν0 to 0 produces stick-slip-like behavior but restricts the choice of the viscosity function; the choice of the viscosity function, in turn, controls both the size of the traction jump associated with changes in velocity and the resulting relaxation back to the equlibrium state.