A sidewall coring apparatus for obtaining a plurality of formation cores from a sidewall of a wellbore includes a core catching tube configured to be sealed downhole and to store the plurality of formation cores therein. The core catching tubes includes an inner sleeve and an outer sleeve concentric with the inner sleeve. The inner and outer sleeves include corresponding slots configured to align in response to relative movement of the inner and outer sleeves, and when aligned the slots of the inner and outer sleeves allow evacuation of fluid from the core catching tube as each of the plurality of formation cores is inserted into the core catching tube.