The Whillans Ice Plain (WIP), Antarctica, experiences twice daily tidally modulated stick‐slip cycles. Slip events last about 30 min, have sliding velocities as high as ∼0.5 mm/s (15 km/yr), and have total slip ∼0.5 m. Slip events tend to occur during falling ocean tide: just after high tide and just before low tide. To reproduce these characteristics, we use rate‐and‐state friction, which is commonly used to simulate tectonic faulting, as an ice stream sliding law. This framework describes the evolving strength of the ice‐bed interface throughout stick‐slip cycles. We present simulations that resolve the cross‐stream dimension using a depth‐integrated treatment of an elastic ice layer loaded by tides and steady ice inflow. Steady sliding with rate‐weakening friction is conditionally stable with steady sliding occurring for sufficiently narrow ice streams relative to a nucleation length. Stick‐slip cycles occur when the ice stream is wider than the nucleation length or, equivalently, when effective pressures exceed a critical value. Ice streams barely wider than the nucleation length experience slow‐slip events, and our simulations suggest that the WIP is in this slow‐slip regime. Slip events on the WIP show a sense of propagation, and we reproduce this behavior by introducing a rate‐strengthening region in the center of the otherwise rate‐weakening ice stream. If pore pressures are raised above a critical value, our simulations predict that the WIP would exhibit quasi‐steady tidally modulated sliding as observed on other ice streams. This study validates rate‐and‐state friction as a sliding law to describe ice stream sliding styles.