An apparatus for securing a package includes a flexible tear-resistant bag and an anchor system for securing the bag to a substrate. The bag includes a receptacle defining a package receiving space and a closure mechanism connected to the receptacle for selectively closing the receptacle. The anchor assembly includes a housing, a fastener, and an anchor securable to the substrate. The housing may be positioned in the package receiving space with the fastener extending through the housing and the receptacle and matingly received in the anchor. A door of the housing may be secured in a closed position to limit access to the fastener. In some embodiments, the bag of the apparatus may also be provided with an alarm system so if an unauthorized entry is attempted by cutting the tear-resistant bag the alarm system will emit an alerting signal.