Abstract: This paper is an evaluation of the potential buildup of boron in the core following the loss of coolant accident for small module reactors. The controlling equation for boron concentration is derived base on the mass conservation of the boron. The potential for boron buildup is evaluated in the short term before automatic depressurization system actuation as well as in the long term during containment recirculation. The results indicate that the passive safety injection systems could prevent the boron from building up significantly in the core and the core from returning to criticality during the long term containment recirculation.