A bag construction for use to distribute flowable material is provided. The bag construction generally includes a first and second panel sections and one or more side gusset panel sections. An internal gusset member may be positioned inside the bag construction, between the first and second panel sections. A tape is disposed inside the bag construction and secures portions of end edges to other sections. In preferred embodiments, a bag construction includes an openable and reclosable closure arrangement and an anti-tamper arrangement.