A self-inflating tire assembly includes a tire having a tire cavity between first and second sidewalls that extend respectively from first and second tire core beads to a tire tread region. At least one of the sidewalls is provided with an air tube peristaltic pump assembly. An air tube has an internal tube air passageway and is positioned within a sidewall groove in contacting engagement with opposite groove surfaces surrounding the air tube. The sidewall groove operatively bends within a rolling tire footprint to compress the air tube from an expanded diameter to a flat diameter adjacent the rolling tire footprint. A core bead passageway extends within a core bead adjacent the one tire sidewall for operatively storing air evacuated from the air tube passageway. Conduits are provided to route air from the air tube to the core bead passageway and valve mechanisms are positioned within the core bead passageway to control the flow of air from the core bead passageway into the tire cavity.